\int {e^{\tan ^{-1} x}}/{1+x^{2}}[(\sec ^{-1} \sqrt{1+x^{2})^{2}+\cos ^{-1}( {1-x^{2}}/{1+x^{2}})] d x=

Correct Answer is : etan−1x(tan−1x)2+C

e^{\tan ^{-1} x}(\tan ^{-1} x)^{2}+C

e^{\tan ^{-1} x}(\sec ^{-1} x)^{2}+C

e^{\tan ^{-1} x}(\sec ^{-1}(\sqrt{1+x^{2}))+C

e^{\tan ^{-1} x}(\cos ^{-1}( {1-x^{2}}/{1+x^{2}}))+C

AP EAPCET 05-Jul-2022 Shift 1 Paper

Section: Mathematics

Question : 71 of 160

Marks: +1, -0

∫‌

etan−1x

1+x2

[(sec−1√1+x2)2+cos−1(‌

1−x2

1+x2

)]dx=

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