integral of cos^2(x)cos(2x)

解

\int cos^{2} (x) cos (2 x) d x

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

解答ステップ

\int cos^{2} (x) cos (2 x) d x

部分積分を適用する

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

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

= \frac{1}{2} cos^{2} (x) sin (2 x) - (- \frac{1}{4} (x - \frac{1}{4} sin (4 x)))

簡素化

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

定数を解答に追加する

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