TS EAMCET · Maths · Indefinite Integration
If \(\int \frac{d x}{x^2+2 x+2}=f(x)+c\), then \(f(x)\) is equal to :
- A \(\tan ^{-1}(x+1)\)
- B \(2 \tan ^{-1}(x+1)\)
- C \(-\tan ^{-1}(x+1)\)
- D \(3 \tan ^{-1}(x+1)\)
Answer & Solution
Correct Answer
(A) \(\tan ^{-1}(x+1)\)
Step-by-step Solution
Detailed explanation
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 \(I=f(x)+c\) \(\therefore \quad f(x)=\tan ^{-1}(x+1)\)
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