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人気のある微分積分 >

integral of 5^xsin(5^x)

解

\int 5^{x} sin (5^{x}) d x

解

- \frac{1}{ln ( 5 )} cos (5^{x}) + C

解答ステップ

\int 5^{x} sin (5^{x}) d x

u置換積分法を適用する

= \int \frac{sin ( u )}{ln ( 5 )} d u

定数を除く:

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

= \frac{1}{ln ( 5 )} \cdot \int sin (u) d u

共通積分を使用する:

\int sin (u) d u = - cos (u)

= \frac{1}{ln ( 5 )} (- cos (u))

代用を戻す

u = 5^{x}

= \frac{1}{ln ( 5 )} (- cos (5^{x}))

簡素化

= - \frac{1}{ln ( 5 )} cos (5^{x})

定数を解答に追加する

= - \frac{1}{ln ( 5 )} cos (5^{x}) + C

グラフ

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