Hopefully I did this one correctly, if anyone sees an error please correct it. This is the problem:
∫(2x+7)/(x2+2x+5)
I rewrote the integral as:
2∫x/(x2+2x+5) + 7∫1/(x2+2x+5)
Both of these parts of the integral is in a form that should be listed in most integral tables in a calculus text book or on-line. From these tables the integral is the following:
2*[(1/2)ln|x2+2x+5| - (1/2)tan-1((2x+2)/4)] + 7*[(1/2)tan-1((2x+2)/4)]
Combining like terms gives the following:
ln|x2+2x+5| + (5/2)*tan-1((2x+2)/4)
(7*sqrt(2))/2 (Seven time the square root of 2, divided by two)
3
If you mean integral[(2x^2 +4x -3)(x+2)], then multiply them out to get: Integral[2x^3+8x^2+5x-6]. This is then easy to solve and is = 2/4x^4+8/3x^3+5/2x^2-6x +c
x3 /12 + 16x + c
2
2
2 times the Square root of 3 + 4
44 divided by (the square root of 4 plus the square root of 4) or 4 divided by point 4 plus 4/4
x/(x+1) = 1 - 1/(x + 1), so the antiderivative (or indefinite integral) is x + ln |x + 1| + C,
Seven.
This integral is a bit complicated to try and type here, so I've included a link to a better representation of it below, under "related links". Also, I assume you do not mean to include the "plus 2" in the square root, as the integral becomes considerably more complicated then.
12.937254