Question

If $\int \frac{dx}{x+x^7}=p\left(x\right)$ then, $\int \frac{x^6}{x+x^7}dx$ is equal to:

• A. $In\left|x\right|-p\left(x\right)+c$
• B. $In\left|x\right|+p\left(x\right)+c$
• C. $x-p\left(x\right)+c$
• D. $x+p\left(x\right)+c$

Answer 1

Answer: (A)

$\int \frac{x^6}{x+x^7}dx=\int \frac{x^6}{x\left(1+x^6\right)}dx$
$=\int \frac{\left(1+x^6\right)-1}{x\left(1+x^6\right)}dx$
$=\int \frac{1}{x}dx-\int \frac{1}{x+x^7}dx$
$=In\left|x\right|-p\left(x\right)+c$