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受欢迎的微积分 >

integral of 6xcos(7x)

解答

\int 6 x cos (7 x) d x

解答

\frac{6}{49} (7 x sin (7 x) + cos (7 x)) + C

求解步骤

\int 6 x cos (7 x) d x

提出常数:

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

= 6 \cdot \int x cos (7 x) d x

使用换元积分法

= 6 \cdot \int \frac{u cos ( u )}{49} d u

提出常数:

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

= 6 \cdot \frac{1}{49} \cdot \int u cos (u) d u

使用分布积分法

= 6 \cdot \frac{1}{49} (u sin (u) - \int sin (u) d u)

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

= 6 \cdot \frac{1}{49} (u sin (u) - (- cos (u)))

u = 7 x

代回

= 6 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x)))

化简

6 \cdot \frac{1}{49} (7 x sin (7 x) - (- cos (7 x))) : \frac{6}{49} (7 x sin (7 x) + cos (7 x))

= \frac{6}{49} (7 x sin (7 x) + cos (7 x))

解答补常数

= \frac{6}{49} (7 x sin (7 x) + cos (7 x)) + C

作图

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