Q113 / 160 · AP EAMCET 2006 · Mathematics

If $\int \frac{d x}{x^2+2 x+2}=f(x)+c$, then $f(x)$ is equal to :

  • Correct answer
    A
    $\tan ^{-1}(x+1)$
  • B
    $2 \tan ^{-1}(x+1)$
  • C
    $-\tan ^{-1}(x+1)$
  • D
    $3 \tan ^{-1}(x+1)$

Solution

Let $I=\int \frac{d x}{x^2+2 x+2}$ $=\int \frac{d x}{x^2+2 x+1+1}=\int \frac{d x}{1+(x+1)^2}$ $=\tan ^{-1}(x+1)+c$ But $I=f(x)+c$ $\therefore \quad f(x)=\tan ^{-1}(x+1)$

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

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