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人気のある微分積分 >

integral of (sin(2)x^2)^2xcos(2)x^2

解

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

解

\frac{sin ^{2} ( 2 )}{8} cos (2) x^{8} + C

解答ステップ

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

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (2) \cdot \int (sin (2) x^{2})^{2} x x^{2} d x

簡素化

(sin (2) x^{2})^{2} x x^{2} : sin^{2} (2) x^{7}

= cos (2) \cdot \int sin^{2} (2) x^{7} d x

定数を除く:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= cos (2) sin^{2} (2) \cdot \int x^{7} d x

べき乗則を適用する

= cos (2) sin^{2} (2) \frac{x ^{8}}{8}

簡素化

cos (2) sin^{2} (2) \frac{x ^{8}}{8} : \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8}

= \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8}

定数を解答に追加する

= \frac{sin ^{2} ( 2 )}{8} cos (2) x^{8} + C

グラフ

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