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受欢迎的微积分 >

integral of 216sin(6x)\sqrt[3]{cos(6x)}

解答

\int 216 sin (6 x) 3 cos (6 x) d x

解答

- 27 cos^{\frac{4}{3}} (6 x) + C

求解步骤

\int 216 sin (6 x) 3 cos (6 x) d x

提出常数:

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

= 216 \cdot \int sin (6 x) 3 cos (6 x) d x

使用换元积分法

= 216 \cdot \int sin (u) 3 cos (u) \frac{1}{6} d u

提出常数:

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

= 216 \cdot \frac{1}{6} \cdot \int sin (u) 3 cos (u) d u

使用换元积分法

= 216 \cdot \frac{1}{6} \cdot \int - 3 v d v

提出常数:

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

= 216 \cdot \frac{1}{6} (- \int 3 v d v)

使用幂法则

= 216 \cdot \frac{1}{6} (- \frac{3}{4} v^{\frac{4}{3}})

代回

= 216 \cdot \frac{1}{6} (- \frac{3}{4} cos^{\frac{4}{3}} (6 x))

化简

216 \cdot \frac{1}{6} (- \frac{3}{4} cos^{\frac{4}{3}} (6 x)) : - 27 cos^{\frac{4}{3}} (6 x)

= - 27 cos^{\frac{4}{3}} (6 x)

解答补常数

= - 27 cos^{\frac{4}{3}} (6 x) + C

作图

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