How do you evaluate int 1/(x+7)(x^2+9) for [-1, 3]?

1 Answer
Sep 16, 2015

-24+58ln(5/3)

Explanation:

the given (x^2+9)/(x+7) can be written as x+(-7x+9)/(x+7)
which can be furthur reduced as x-7+58/(x+7)
int_ -1^3x-7+58/(x+7)dx=int_-1^3(x^2+9)/(x+7)dx
int_ -1^3xdx-7dx+58/(x+7)dx
x^2/2-7x+58ln(x+7)from [-1 3]
9/2-7*3+58ln10-(1/2-7*(-1)+58ln6)
4-28+58ln(10/6)
-24+58ln(5/3)
ln stands for Natural Logarithm log_e(x)