JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \frac{\sin x+\cos x}{9+16 \sin 2 x} d x

is equal to

View answer and explanation

Correct option: A

\frac{1}{40} \ln \left|\frac{5+4(\sin x-\cos x)}{5-4(\sin x-\cos x)}\right|+c

Option A (

\frac{{1}}{{40}} \ln \left| {\frac{{5 + 4(\sin x - \cos x)}}{{5 - 4(\sin x - \cos x)}}} \right| + c

) is correct because the integral is solved by substitution using

t = \sin x - \cos x

More Questions from INDEFINITE INTEGRATION

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

f(x)

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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

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{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