JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Analyzing +4 | -1

\int e^{\sin x} \frac{\left(x \cos ^3 x-\sin x\right)}{\cos ^2 x} d x

is equal to

View answer and explanation

Correct option: C

e^{\sin x}(x-\sec x)+c

Option B (

\frac{{(x+1) e^x}}{{x^2+1}}+c

) is correct because the integral can be expressed in the form

\int e^x [f(x) + f'(x)] dx

, where

f(x) = \frac{{x+1}}{{x^2+1}}

and its derivative is

\frac{{1-2x-x^2}}{{(x^2+1)^2}}

More Questions from INDEFINITE INTEGRATION

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\int \sin ^5 x \cos ^4 x d x=

f(x)

\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

f\left(\frac{4}{25}\right)

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

f(1)

{C}

\int \frac{x^7}{\left(1-x^2\right)^5} d x

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx