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受欢迎的微积分 >

integral of x^2cos(4x^3-1)

解答

\int x^{2} cos (4 x^{3} - 1) d x

解答

\frac{1}{12} sin (4 x^{3} - 1) + C

求解步骤

\int x^{2} cos (4 x^{3} - 1) d x

使用换元积分法

= \int \frac{cos ( 4 u - 1 )}{3} d u

提出常数:

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

= \frac{1}{3} \cdot \int cos (4 u - 1) d u

使用换元积分法

= \frac{1}{3} \cdot \int cos (v) \frac{1}{4} d v

提出常数:

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

= \frac{1}{3} \cdot \frac{1}{4} \cdot \int cos (v) d v

使用积分常见定则:

\int cos (v) d v = sin (v)

= \frac{1}{3} \cdot \frac{1}{4} sin (v)

代回

= \frac{1}{3} \cdot \frac{1}{4} sin (4 x^{3} - 1)

化简

\frac{1}{3} \cdot \frac{1}{4} sin (4 x^{3} - 1) : \frac{1}{12} sin (4 x^{3} - 1)

= \frac{1}{12} sin (4 x^{3} - 1)

解答补常数

= \frac{1}{12} sin (4 x^{3} - 1) + C

作图

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