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受欢迎的微积分 >

integral of 3(sqrt(x))cos(x/3)

解答

\int 3 (x) cos (\frac{x}{3}) d x

解答

93 (\frac{x}{3} sin (\frac{x}{3}) - \frac{π}{2} § (\frac{2}{π} \frac{x}{3})) + C

求解步骤

\int 3 x cos (\frac{x}{3}) d x

提出常数:

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

= 3 \cdot \int x cos (\frac{x}{3}) d x

使用换元积分法

= 3 \cdot \int 33 u cos (u) d u

提出常数:

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

= 3 \cdot 33 \cdot \int u cos (u) d u

使用分布积分法

= 3 \cdot 33 (u sin (u) - \int \frac{sin ( u )}{2 u} d u)

\int \frac{sin ( u )}{2 u} d u = \frac{π}{2} § (\frac{2}{π} u)

= 3 \cdot 33 (u sin (u) - \frac{π}{2} § (\frac{2}{π} u))

u = \frac{x}{3}

代回

= 3 \cdot 33 (\frac{x}{3} sin (\frac{x}{3}) - \frac{π}{2} § (\frac{2}{π} \frac{x}{3}))

化简

= 93 (\frac{x}{3} sin (\frac{x}{3}) - \frac{π}{2} § (\frac{2}{π} \frac{x}{3}))

解答补常数

= 93 (\frac{x}{3} sin (\frac{x}{3}) - \frac{π}{2} § (\frac{2}{π} \frac{x}{3})) + C

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\frac{\partial}{\partial z} (e^{- x^{2} - 2 y^{2} - 3 z^{2}})