A) \[{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]
B) \[\frac{1}{2}{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]
C) \[2{{[{{\tan }^{-1}}{{x}^{2}}]}^{2}}+C\]
D) None of above
Correct Answer: B
Solution :
Put \[t={{\tan }^{-1}}{{x}^{2}}\] \[\Rightarrow \] \[dt=\frac{1}{1+{{x}^{4}}}2xdx,\]then \[\int_{{}}^{{}}{\frac{2x{{\tan }^{-1}}{{x}^{2}}}{1+{{x}^{4}}}}dx=\int_{{}}^{{}}{fdt=\frac{{{t}^{2}}}{2}+C}\] \[=\frac{1}{2}{{({{\tan }^{-1}}{{x}^{2}})}^{2}}+C\]
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