Find the value of (1+x) (1+x^2 )(1-x) d x : - Vidyadip

Question

Find the value of $\int(1+x)\left(1+x^2\right)(1-x) d x$ :

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Answer

$
\begin{array}{l}
\int(1+x)\left(1+x^2\right)(1-x) d x \\
\Rightarrow \int(1+x)(1-x)\left(1+x^2\right) d x \\
\Rightarrow \int\left(1-x^2\right)\left(1+x^2\right) d x \\
\Rightarrow \int\left(1-x^4\right) d x=\int d x-\int x^4 d x \\
\Rightarrow x-\frac{x^5}{5}+C
\end{array}
$

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