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受欢迎的微积分 >

integral of 1/3*x^3cos(x^4+2)

解答

\int \frac{1}{3} \cdot x^{3} cos (x^{4} + 2) d x

解答

\frac{1}{12} sin (x^{4} + 2) + C

求解步骤

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

提出常数:

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

= \frac{1}{3} \cdot \int x^{3} cos (x^{4} + 2) d x

使用换元积分法

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

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 (u) d u

使用积分常见定则:

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

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

u = x^{4} + 2

代回

= \frac{1}{3} \cdot \frac{1}{4} sin (x^{4} + 2)

化简

\frac{1}{3} \cdot \frac{1}{4} sin (x^{4} + 2) : \frac{1}{12} sin (x^{4} + 2)

= \frac{1}{12} sin (x^{4} + 2)

解答补常数

= \frac{1}{12} sin (x^{4} + 2) + C

作图

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