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受欢迎的微积分 >

integral of-xcos(3x)

解答

\int - x cos (3 x) d x

解答

- \frac{1}{9} (3 x sin (3 x) + cos (3 x)) + C

求解步骤

\int - x cos (3 x) d x

提出常数:

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

= - \int x cos (3 x) d x

使用换元积分法

= - \int \frac{u cos ( u )}{9} d u

提出常数:

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

= - \frac{1}{9} \cdot \int u cos (u) d u

使用分布积分法

= - \frac{1}{9} (u sin (u) - \int sin (u) d u)

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

= - \frac{1}{9} (u sin (u) - (- cos (u)))

u = 3 x

代回

= - \frac{1}{9} (3 x sin (3 x) - (- cos (3 x)))

化简

= - \frac{1}{9} (3 x sin (3 x) + cos (3 x))

解答补常数

= - \frac{1}{9} (3 x sin (3 x) + cos (3 x)) + C

作图

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