Integral Calculus Question 346
Question: $ \int{\frac{{{(x+1)}^{2}}dx}{x(x^{2}+1)}} $ is equal to
[MP PET 2003]
Options:
A) $ {\log_{e}}x+c $
B) $ {\log_{e}}x+2{{\tan }^{-1}}x+c $
C) $ {\log_{e}}\frac{1}{x^{2}+1}+c $
D) $ {\log_{e}}{x(x^{2}+1)}+c $
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Answer:
Correct Answer: B
Solution:
$ \int{\frac{{{(x+1)}^{2}}}{x(x^{2}+1)}dx} $ $ =\int{\frac{x^{2}+1+2x}{x(x^{2}+1)}dx} $ $ =\int{\frac{x^{2}+1}{x(x^{2}+1)}dx+2\int{\frac{x}{x(x^{2}+1)}dx}} $ $ =\int{\frac{dx}{x}+2\int{\frac{dx}{x^{2}+1}}}={\log_{e}}x+2{{\tan }^{-1}}x+c $ .
BETA
