Answer
$\displaystyle\int\frac{(x+4)}{(x^{2}+8x-7)^{2}}$ dx =$-\frac{1}{2(x^{2}+8x-7)}$ +c where c is an arbitrary constant
Work Step by Step
To solve this integral, we will attempt to find the derivative and antiderivative pair.
$\frac{d}{dx}(x^{2}+8x-7)^{-1}$=(-1)$(x^{2}+8x-7)^{-2}(2x+8)$
=$\frac{-2(x+4)}{(x^{2}+8x-7)^{2}}$
Therefore, $\int\frac{(x+4)}{(x^{2}+8x-7)^{2}}$ dx = -$\frac{1}{2}\int\frac{-2(x+4)}{(x^{2}+8x-7)^{2}}$ dx
=-$\frac{1}{2(x^{2}+8x-7)}$ +c where c is an arbitrary constant
