$\int \frac{1}{(x+2)(1+x)^2} \mathrm{~d} x$ has the value

$\int \frac{1}{(x+2)(1+x)^2} \mathrm{~d} x$ has the value
  1. $2 \log \left(\frac{x+2}{x^2+1}\right)+4 \tan ^{-1} x+\mathrm{c}$, where $\mathrm{c}$ is a constant of integration.
  2. $\log \frac{x+2}{x^2+1}-4 \tan ^{-1} x+\mathrm{c}$, where $\mathrm{c}$ is a constant of integration.
  3. $\log \frac{(x+2)^2}{\left(x^2+1\right)}+4 \tan ^{-1} x+\mathrm{c}$, where $\mathrm{c}$ is a constant of integration.
  4. $\log \frac{(x+2)}{\left(x^2+1\right)^2}-4 \tan ^{-1} x+\mathrm{c}$, where $\mathrm{c}$ is a constant of integration.

Solution

Std.12 $\mid$ Part-2 $\mid$ Ch-3 $\mid$ Exercise-3.4 [Note: The question cannot be solved due to insufficient data.]

Asked in: MHT CET 2023 (12 May Shift 2)

Practice more Indefinite Integration questions on Aicharya