Question

The value of $I=\int \frac{x}{x+1}dx$ is :

• A. $\frac{\pi }{2}\log 2$
• B. $\log 2$
• C. $\pi \log 2$
• D. none of these.

Answer 1

The correct option is D none of these.

We have,

$I=\int \frac{x}{x+1}dx$

$I=\int \frac{x+1-1}{x+1}dx$

$I=\int 1dx-\int \frac{1}{x+1}dx$

$I=x-\ln (x+1)+C$

Hence, option $D$ is the correct answer.