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\(\int \frac{(x+1)^2}{x\left(x^2+1\right)} d x=\)
Options:
Solution:
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Verified Answer
The correct answer is:
\(\log |x|+2 \tan ^{-1}(x)+c\)
\(\begin{aligned}
I & =\int \frac{(x+1)^2}{x\left(x^2+1\right)} d x=\int \frac{\left(x^2+1\right)+2 x}{x\left(x^2+1\right)} d x \\
& =\int \frac{1}{x} d x+2 \int \frac{d x}{x^2+1}=\log _e|x|+2 \tan ^{-1} x+C
\end{aligned}\)
Hence, option (c) is correct.
I & =\int \frac{(x+1)^2}{x\left(x^2+1\right)} d x=\int \frac{\left(x^2+1\right)+2 x}{x\left(x^2+1\right)} d x \\
& =\int \frac{1}{x} d x+2 \int \frac{d x}{x^2+1}=\log _e|x|+2 \tan ^{-1} x+C
\end{aligned}\)
Hence, option (c) is correct.
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