JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

u=\int e^{a x} \sin b x \,d x

and

v=\int e^{a x} \cos b x \,d x

, then

\tan ^{-1}\left(\frac{u}{v}\right)+\tan ^{-1}\left(\frac{b}{a}\right)

equals

View answer and explanation

Correct option: A

b x

Option A,

b x

, is correct because by expressing

u

and

v

in terms of trigonometric functions and using the arctangent addition formula, the expression simplifies to

bx

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