\[ \int \frac{e^{\tan ^{-1} x}}{\left(1+x^{2}\right)}\left[\left(\s...

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\[
\int \frac{e^{\tan ^{-1} x}}{\left(1+x^{2}\right)}\left[\left(\sec ^{-1} \sqrt{1+x^{2}}\right)^{2}+\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)\right] d x
\]
\( \mathrm{P} \)
W
\( (x0) \)
(1) \( e^{\tan ^{-1} x} \cdot \tan ^{-1} x+C \)
(2) \( \frac{e^{\tan ^{-1} x} \cdot\left(\tan ^{-1} x\right)^{2}}{2}+C \)
(3) \( e^{\tan ^{-1} x} \cdot\left(\sec ^{-1}\left(\sqrt{1+x^{2}}\right)\right)^{2}+C \)
(4) \( e^{\tan ^{-1} x} \cdot\left(\operatorname{cosec}^{-1}\left(\sqrt{1+x^{2}}\right)\right)^{2}+C \)
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