Quantcast
answersLogoWhite
notificationBell

Top Answer
User Avatar
Wiki User
Answered 2013-03-07 19:16:03

Assume the expression is:

∫ sin(x)x²e^x dx

Then:

Take the integral: integral e^x x^2 sin(x) dx For the integrand e^x x^2 sin(x), integrate by parts, integral f dg = f g- integral g df, where f = x^2, dg = e^x sin(x) dx, df = 2 x dx, g = 1/2 e^x (sin(x)-cos(x)): = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral e^x x (sin(x)-cos(x)) dx Expanding the integrand e^x x (sin(x)-cos(x)) gives e^x x sin(x)-e^x x cos(x): = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral (e^x x sin(x)-e^x x cos(x)) dx Integrate the sum term by term and factor out constants: = 1/2 e^x x^2 sin(x)-1/2 (e^x x^2 cos(x))- integral e^x x sin(x) dx+ integral e^x x cos(x) dx For the integrand e^x x sin(x), integrate by parts, integral f dg = f g- integral g df, where f = x, dg = e^x sin(x) dx, df = dx, g = 1/2 e^x (sin(x)-cos(x)): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+ integral e^x x cos(x) dx+1/2 integral e^x (sin(x)-cos(x)) dx Expanding the integrand e^x (sin(x)-cos(x)) gives e^x sin(x)-e^x cos(x): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+ integral e^x x cos(x) dx+1/2 integral (e^x sin(x)-e^x cos(x)) dx Integrate the sum term by term and factor out constants: = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)+1/2 e^x x cos(x)+1/2 integral e^x sin(x) dx-1/2 integral e^x cos(x) dx+ integral e^x x cos(x) dx For the integrand e^x cos(x), use the formula integral exp(alpha x) cos(beta x) dx = (exp(alpha x) (alpha cos(beta x)+beta sin(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/4 e^x sin(x)-1/2 e^x x sin(x)-1/4 (e^x cos(x))+1/2 e^x x cos(x)+1/2 integral e^x sin(x) dx+ integral e^x x cos(x) dx For the integrand e^x sin(x), use the formula integral exp(alpha x) sin(beta x) dx = (exp(alpha x) (alpha sin(beta x)-beta cos(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x x sin(x)-1/2 (e^x cos(x))+1/2 e^x x cos(x)+ integral e^x x cos(x) dx For the integrand e^x x cos(x), integrate by parts, integral f dg = f g- integral g df, where f = x, dg = e^x cos(x) dx, df = dx, g = 1/2 e^x (sin(x)+cos(x)): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral e^x (sin(x)+cos(x)) dx Expanding the integrand e^x (sin(x)+cos(x)) gives e^x sin(x)+e^x cos(x): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral (e^x sin(x)+e^x cos(x)) dx Integrate the sum term by term: = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)+e^x x cos(x)-1/2 e^x cos(x)-1/2 integral e^x sin(x) dx-1/2 integral e^x cos(x) dx For the integrand e^x cos(x), use the formula integral exp(alpha x) cos(beta x) dx = (exp(alpha x) (alpha cos(beta x)+beta sin(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/4 e^x sin(x)+e^x x cos(x)+-3/4 e^x cos(x)-1/2 integral e^x sin(x) dx For the integrand e^x sin(x), use the formula integral exp(alpha x) sin(beta x) dx = (exp(alpha x) (alpha sin(beta x)-beta cos(beta x)))/(alpha^2+beta^2): = 1/2 e^x x^2 sin(x)-1/2 e^x x^2 cos(x)-1/2 e^x sin(x)+e^x x cos(x)-1/2 e^x cos(x)+constant Which is equal to: Answer: | | = 1/2 e^x ((x^2-1) sin(x)-(x-1)^2 cos(x))+constant

001
๐Ÿ™๐Ÿฟ
0
๐Ÿคจ
0
๐Ÿ˜ฎ
0
๐Ÿ˜‚
0
User Avatar

Your Answer

Still Have Questions?

Related Questions

How do you differentiate exp exp exp x?

By using the chain rule. Since the derivative of exp(x) is exp(x), the derivative of exp(exp(exp(x))) is exp(exp(exp(x))) times the derivative of what is inside the parentheses, i.e., exp(exp(exp(x))) times derivate of exp(exp(x)). Continue using the chain rule once more, for this expression.



What is 0.989 in scientific notation?

9.89 exp-1 (9.89 times 10 to the -1 power)



What is the best way to train Magikarp?

Give him an EXP SHARE, and go trough the pokémon league (a couple of times) Use an other pokémon, not magikarp, but keep him in your team. He will get EXP without battling.


How do you make poliwrath lv100?

I suggest you give poliwrath the exp share and go through the elite 4 a bunch of times


Do Pokemon get boosted exp if you trade them?

Yes they do(1.5 times the exp a regularly caught Pokemon will get), but if they are a higher level of your badge alows them to listen to you, they will use random moves,ignore orders, don't listen to you, and fall asleep in the middle of battles.


Does being good at math literally help you in chemistry?

No, it doesn't help you 'literally' but it is convenient because chemistry uses a lot of calculation: generally 'solving equations' most commonly + - : x log less commonly exp 'square root' integral/differential etc.


What quests do you get a lot of exp from in dragonfbale?

Do bounty hunting lot of times until u come to an enemy which gives ya 600 gold(maximum)


What do you do after having got the exp share in Pokemon silver?

You can give it to a Pokemon you want to lvl up fasterit give two times the experience point


Where is the best place to train Pokemon in Pokemon black?

Exp share at elite four a couple times that's how i got a lv. 100 tepig



How do you train Pokemon quick?

to train your Pokemon quick you need to get a exp share by getting a red scale then trading it with mr.pokemons exp share.then give it to your Pokemon and then beat all the gym leaders/red and then beat the elite four a couple of times simple


How is xex and xe2x integrated manually?

The definite integral of the function f=x*exp(k*x) is (1/k)*(x-(1/k))*exp(k*x). So you have the answer to your questions by setting k equal to 1 then 2. I derived my formula by using integration by parts, setting u=x and dv=exp(k*x)dx.


How do you enter scientific notation into a calculator?

First of all, you have to have a scientific calculator, one that supports scientific notation. (As far as I know, all scientific calculators do.) The scientific calculator should have a special key labelled something like EXP. To input (for example) 2.3 million, you would type 2.3 EXP 6 (where EXP is short for "times 10 to the power...").


Why are negative square roots are on the real number line if square root of a negative number not a real number?

Negative square roots are just the opposite of positive square roots. Since square roots (of positive numbers) are real, the negative square roots are also real.Square roots of negative numbers are not real.Note that -1 = exp(Pi*i), so (-1)^(1/2) = exp((1/2)*Pi*i) = i.Note that exp(i*x) = cos(x) + i*sin(x), for instance by taking derivatives:(d/dx)(exp(i*x)) = i*exp(i*x), and(d/dx)^2(exp(i*x)) =(-1)*exp(i*x).This means that the second derivative of exp(i*x) equals -exp(i*x).The same property holds for cos(x) + i*sin(x):(d/dx)(cos(x) + i*sin(x)) = -sin(x) + i*cos(x)(d/dx)^2(cos(x) + i*sin(x)) = -cos(x) - i*sin(x) = -(cos(x) + i*sin(x)))Hence cos(x) + i*sin(x)) = C + Dx + exp(i*x), for some C and D.Comparing the values on both sides for x = 0, we find:1 = C+1, so C = 0 and for the first derivative:i = D + i, so D = 0.So cos(x) + i*sin(x)) = exp(i*x) for all x.by comparing x=0 for both functions and their first derivative. Since they coincide,


How do you express hypoexponential distribution in terms of exponential distribution?

The hypoexponential distribution is two or more exponential distribution convolved together, so:hypo[x] = integral of A*exp(-A*x)*B*exp(-B*(t-x)) from 0 to t.If you have more stages you do more convolutions.


Integration of exponential of square of x?

its an non integrable functionThe indefinite integral of exp(x^2) dx is1/2 * sqrt(pi) * erfi(x) + Kwhere erfi(x) is the imaginary error function, defined with regard to the error function aserfi(x) = - i erf(ix)see http://mathworld.wolfram.com/Erfi.htmlAlso, try wolframalpha.com, enterexp(x^2) in the search box orint(exp(x^2),x)to see some plots and other info.Answere^(x^2) is an example of a function expressible using standard functions (+, *, exp, log, atan, etc) whose integral can not be expressed in this way. In such cases we invent a name for the function defined by the interval, but it's just a name and doesn't shed any light on the function. In short, there is no intellectually satisfying answer to this question.


How do you get Dead Frontier back on 2d version?

It is most certainly NOT impossible like people would suggest although it isn't logical because every time you go to a new area your exp goes down to 0% and your exp goes down to 0% at random times.


What is is the base face of a square pyramid?

A square pyramid's base is a square. You can tell by the name (for exp. a triangular pyramid's base is a triangle.) Good luck with whatever you need it for :)


On naruto arena do you lose more xp when you surrender or defeated and if anyone fights deidara-sensai make sure to surrender cause im trying to beat a mission but i have lost 3 times in a row?

The amount of exp you lose depends on if your oppent is a higher or lower rank than you. If he is higher, you will not lose much exp, if his lvl is lower, you will lose more exp. Note: You only lose/earn exp on LADDER MATCHES.



What quests on RuneScape give you thieving exp?

The following Quests give you thieving XP:-Mourning's End part 1 - 25,000 expRocking out - 25,000 expThe Chosen Commander - 20,000 expThe Feud - 15,000 expCurse of Arrav- 14,000 expContact - 7,000 expDarkness of Hallovale- 6,000 expDealing with Scabaras- level 7,000 expGrim Tales - 6,000 expThe path of Glouphrie - 5,000 expIcthlarin's Little Helper- 4,500 expRat Catcher - 4,500 expSlug Menace- 3,500 expFight Arena- 3,375 expLand of Goblins - 3,000 expFermanik Trials- 2,813 expFairy tale part2: Cure a Queen - 2,500 expDeath to Dorgeshunn - 2,000 expHunt for Red Raktuber- 2,000 expHazeel Cult- 1,500 expBiohazard - 1,500 expTribal Totem- 1,250 expThe Golem- 1,000 expCreature of Fenkenstrain- 1,000 expSpirits of the Elid - 1,000 expHand in the Sand - 1,000 expPerils of Ice Mountain - 500 expTower of Life - 500 exp


How do you get exp on binweevil?

you can cheat by playing 2 balls lots of times but get someone to let u win so many times its the best way to get exp trust me, don't use cheat engines because they hack ur PC and get a virus into it. kitkat tried the cheat engine but thankfully in her frineds PC lol he got a virus in there but it recovered by deleting the program/software anyways hope i asnwerd ur queston


How do you get exp in halo when you have negative exp?

you go up exp by winning and lose exp by quitting


Still have questions?

Trending Questions
What times 10 equals to 1000? Asked By Wiki User
How old is Danielle cohn? Asked By Wiki User
Previously Viewed
Unanswered Questions