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受欢迎的微积分 >

integral of (4x^2)/(sqrt(x^3+16))

解答

\int \frac{4 x ^{2}}{x ^{3} + 16} d x

解答

\frac{8}{3} x^{3} + 16 + C

求解步骤

\int \frac{4 x ^{2}}{x ^{3} + 16} d x

提出常数:

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

= 4 \cdot \int \frac{x ^{2}}{x ^{3} + 16} d x

使用换元积分法

= 4 \cdot \int \frac{2}{3} d u

常数积分:

\int a d x = a x

= 4 \cdot \frac{2}{3} u

u = x^{3} + 16

代回

= 4 \cdot \frac{2}{3} x^{3} + 16

化简

4 \cdot \frac{2}{3} x^{3} + 16 : \frac{8}{3} x^{3} + 16

= \frac{8}{3} x^{3} + 16

解答补常数

= \frac{8}{3} x^{3} + 16 + C

作图

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