, ( ) is equal to

MATHEMATICS · Single correct · A Level · Mathematics · Integration · Integration

Problem

\int \frac{e^{\tan^{-1} x}}{(1+x^2)} \left[ (\sec^{-1} \sqrt{1+x^2})^2 + \cos^{-1} \left( \frac{1-x^2}{1+x^2} \right) \right] dx

, (

x > 0

) is equal to (1)

e^{\tan^{-1} x} \cdot \tan^{-1} x + C

(2)

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

(3)

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

(4)

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