Question

State whether the following statement is true or false.

$\int \frac{x^2}{1+x^3}dx=\frac{log(x^3+1)}{3}+c$

• A. True
• B. False

Answer 1

The correct option is A True

Given,

$\int \frac{x^2}{1+x^3}dx$

apply u substitution: $u=1+x^3$ and $du=3x^{2}dx\Rightarrow dx=\frac{du}{3x^2}$

$=\int \frac{1}{3u}du$

$=\frac{1}{3}\log \left|u\right|$

$=\frac{1}{3}\log (1+x^3)+c$