If $\int \frac{1}{x^2+2 x+2} d x=f(x)+C$

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Indefinite Integration

Question:

If $\int \frac{1}{x^2+2 x+2} d x=f(x)+C$, then $f(x)=$

Options:

$\tan ^{-1}(x+1)$

$2 \tan ^{-1}(x+1)$

$-\tan ^{-1}(x+1)$

$3 \tan ^{-1}(x+1)$

Correct Answer:

$\tan ^{-1}(x+1)$

Explanation:

We have,

$\int \frac{1}{x^2+2 x+2} d x=\int \frac{1}{(x+1)^2+1^2} d x=\tan ^{-1}(x+1)+C$

$f(x)=\tan ^{-1}(x+1)$