Math and Arithmetic
Calculus

What is the antiderivative of e to the x plus 17?

Wiki User

I'm not sure if you mean e^x + 17 or e^(x+17) so we'll do both.

First, the integral of e^x + 17

because these terms are being added you can integrate them separately:

integral((e^x)dx) + integral(17dx)

integral of e^x is just e^x + C

Integral of 17 is 17x + C, so we get:

e^x + 17x + C

Second, the integral of e^(x+17)

we know how to integrate the form e^u, so just do a u substitution

u=x+17

du=dx

so we get

integral((e^u)du)=e^u + C

resubstitute for u and get e^(x+17) + C

🙏
0
🤨
0
😮
0
😂
0

Related Questions

What is the antiderivative of xex?

One can use integration by parts to solve this. The answer is (x-1)e^x.

What is the antiderivative of e to the power of one divided by -x?

Powers of e are simple to integrate. The derivative of eu equals u'eu; inversely, the antiderivative of eu equals eu/u'. Therefore, the antiderivative of e1/-x equals (e1/-x)/{d/dx[1/-x]}. The derivative of 1/-x, which can also be expressed as x-1, equals (-1)x(-1-1) = -x-2 = -1/x2.

Integral of e to the power of x?

The antiderivative, or indefinite integral, of ex, is ex + C.

What is the antiderivative of x to the -1?

Antiderivative of x/-1 = -1(x^2)/2 + C = (-1/2)(x^2) + C Wolfram says antiderivative of x^-1 is log(x) + C

What is the antiderivative of x to the 1?

By antiderivative do you mean integral? If yes, integral x^1 dx= (x^2)/2

What is the antiderivative of e to the power of one divided by x?

1/ln(x)*e^(1/x) if you differentiate e^(1/x), you will get ln(x)*e^(1/x). times this by 1/ln(x) and you get you original equation. Peace

sqrt(1) + 3*sqrt(x) = 1 + 3*x^1/2So the antiderivative is x + [3*x^(3/2)]/(3/2) + c = x + 2*x^(3/2) + c where c is the constant of integration.

How do you solve g x equals -3x plus 1?

If: x = -3x+1 Then: x+3x = 1 =&gt; 4x =1 So: x = 1/4 or 0.25 ----------- I notice that the question requests a solution for g x = -3x + 1. It seems possible that parentheses around the 'x' after the 'g' have gone missing, along with a prime indicating the derivative of the function g. This being the case, we would be seeking the antiderivative of -3x + 1. The antiderivative of a sum is the sum of the antiderivatives. So we can look at -3x and +1 separately. The derivative of x2 is 2x. Therefore, the antiderivative of x is x2/2, and the antiderivative of -3x is -3x2/2. The antiderivative of 1 is x. Overall, the solution is the antiderivative -3x2/2 + x + C, where C is an arbitrary constant.

What is the antiderivative of x to the negative 6 5ths?

(that weird integral or antiderivative sign) x^(-6/5) dx =-5*x^(-1/5)

What is the integral of x divided by x plus 1?

x/(x+1) = 1 - 1/(x + 1), so the antiderivative (or indefinite integral) is x + ln |x + 1| + C,

Is there any other anti derivative of 1 divided by x?

The antiderivative of 1/x is ln(x) + C. That is, to the natural (base-e) logarithm, you can add any constant, and still have an antiderivative. For example, ln(x) + 5. These are the only antiderivatives; there are no different functions that have the same derivatives. This is valid, in general, for all antiderivatives: if you have one antiderivative of a function, all other antiderivatives are obtained by adding a constant.

How do you take the antiderivative of 1 over x?

The general formula for powers doesn't work in this case, because there will be a zero in the denominator. The antiderivative of 1/x is ln(x), that is, the natural logarithm of x.

4x plus 17 equals x plus 2?

4x + 17 = x + 2 4x - x = 2 - 17 3x = -15 x = -5

What has the same answer as 17 plus x equal?

x + 17, perhaps.x + 17, perhaps.x + 17, perhaps.x + 17, perhaps.

How can you calculate the arbitrary constant in the solution to an antiderivative?

You can't, unless it's an initial value problem. If f(x) is an antiderivative to g(x), then so is f(x) + c, for any c at all.

What is the antiderivative of pi?

The anti-derivative of any constant c, is just c*x. Thus, the antiderivative of pi is pi*x. We can verify this by taking the derivative of pi*x, which gives us pi.

What is the antiderivative of square root of x plus 1?

sqrt(X + 1) is also; (X + 1)^1/2 ( add 1 to exponent and multiply by inverse ) 2/3(X +1)^3/2

What is the antiderivative of sqrtx plus 4ex minus sinx?

The anti-derivative of sqrt(x) : sqrt(x)=x^(1/2) The anti-derivative is x^(1/2+1) /(1/2+1) = (2/3) x^(3/2) The anti-derivative is 4e^x is 4 e^x ( I hope you meant e to the power x) The anti-derivative of -sin(x) is cos(x) Adding, the anti-derivative is (2/3) x^(3/2) + 4 e^x + cos(x) + C

Still have questions?

Trending Questions
Previously Viewed