integral of 1/((x+1)^{1/3)}

解答

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

\frac{3}{2} (x + 1)^{\frac{2}{3}} + C

求解步骤

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

使用换元积分法

= \int \frac{1}{u ^{\frac{1}{3}}} d u

使用幂法则

= \frac{3}{2} u^{\frac{2}{3}}

u = x + 1

代回

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

解答补常数

= \frac{3}{2} (x + 1)^{\frac{2}{3}} + C

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