Q114 / 180 · COMEDK 2016 · Mathematics

$\int \frac{\left(x^{3}+3 x^{2}+3 x+1\right)}{(x+1)^{5}} d x=$

  • A
    $\tan ^{-1} x+c$
  • B
    $\log (x+1)+c$
  • C
    $\frac{1}{5} \log (x+1)+c$
  • Correct answer
    D
    $-\frac{1}{(x+1)}+c$

Solution

$\int \frac{x^{3}+3 x^{2}+3 x+1}{(x+1)^{5}} d x$ $\begin{aligned} &=\int \frac{(x+1)^{3}}{(x+1)^{5}} d x=\int \frac{d x}{(x+1)^{2}} \\ &=-\frac{1}{x+1}+c \end{aligned}$

Hence, the correct answer is option: 'D'.

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