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受欢迎的微积分 >

integral of (x^2+2x+1)^{20}

解答

\int (x^{2} + 2 x + 1)^{20} d x

解答

\frac{( x + 1 ) ^{41}}{41} + C

求解步骤

\int (x^{2} + 2 x + 1)^{20} d x

对

x^{2} + 2 x + 1

配方:

(x + 1)^{2}

= \int ((x + 1)^{2})^{20} d x

使用换元积分法

= \int u^{40} d u

使用幂法则

= \frac{u ^{41}}{41}

u = x + 1

代回

= \frac{( x + 1 ) ^{41}}{41}

解答补常数

= \frac{( x + 1 ) ^{41}}{41} + C

作图

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