integral of x^2(10^{x^3})

解答

\int x^{2} (1 0^{x^{3}}) d x

\frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}} + C

求解步骤

\int x^{2} \cdot 1 0^{x^{3}} d x

使用换元积分法

= \int \frac{1}{3 ln ( 10 )} d u

常数积分:

\int a d x = a x

= \frac{1}{3 ln ( 10 )} u

u = 1 0^{x^{3}}

代回

= \frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}}

解答补常数

= \frac{1}{3 ln ( 10 )} \cdot 1 0^{x^{3}} + C

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