integral of 7^xsin(7^x)

解答

\int 7^{x} sin (7^{x}) d x

- \frac{1}{ln ( 7 )} cos (7^{x}) + C

求解步骤

\int 7^{x} sin (7^{x}) d x

使用换元积分法

= \int \frac{sin ( u )}{ln ( 7 )} d u

提出常数:

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

= \frac{1}{ln ( 7 )} \cdot \int sin (u) d u

使用积分常见定则:

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

= \frac{1}{ln ( 7 )} (- cos (u))

u = 7^{x}

代回

= \frac{1}{ln ( 7 )} (- cos (7^{x}))

化简

= - \frac{1}{ln ( 7 )} cos (7^{x})

解答补常数

= - \frac{1}{ln ( 7 )} cos (7^{x}) + C

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