(x+1 x )^3 d x= - Vidyadip

MCQ

$\int\left(x+\frac{1}{x}\right)^3 d x=$

A
$\frac{1}{4}\left(x+\frac{1}{x}\right)^4+c$
✓
$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$
C
$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x+\frac{1}{x^2}+c$
D
$\left(x-x^{-1}\right)^3+c$

✓

Answer

Correct option: B.

$\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$

(b) $\frac{x^4}{4}+\frac{3 x^2}{2}+3 \log x-\frac{1}{2 x^2}+c$
Hint:
$
\left(x+\frac{1}{x}\right)^3=x^3+3 x+\frac{3}{x}+\frac{1}{x^3}
$

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