Check the solution to "Evaluate the integral. ∫cos2xsin⁡2xdx"

Bevan Mcdonald

Answered question

2021-11-09

Evaluate the integral.

\int \cos^{2} x \sin 2 x d x

Demi-Leigh Barrera

Skilled2021-11-10Added 97 answers

Step 1
Given :

\int \cos^{2} x \sin 2 x d x

Step 2
We have to evaluate given integral.

\int \cos^{2} x \sin 2 x d x

put

u = \cos^{2} x

d u = - \sin 2 x d x

d x = - \frac{d u}{\sin 2 x}

= \int - u d u

= - \int u d u

= - \frac{u^{1 + 1}}{1 + 1} + C

= - \frac{u^{2}}{2} + C

put

u - \cos^{2} x

= - \frac{{(\cos^{2} x)}^{2}}{2} + C

= \frac{- 1}{2} \cos^{4} x + C

\int \cos^{2} (x) \sin (2 x) d x = - \frac{1}{2} \cos^{4} (x) + C

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