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受欢迎的微积分 >

integral from 0 to 1 of 3x^2(1+x^3)^5

解答

\int_{0}^{1} 3 x^{2} (1 + x^{3})^{5} d x

解答

\frac{21}{2}

+1

十进制

10.5

求解步骤

\int_{0}^{1} 3 x^{2} (1 + x^{3})^{5} d x

提出常数:

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

= 3 \cdot \int_{0}^{1} x^{2} (1 + x^{3})^{5} d x

使用换元积分法

= 3 \cdot \int_{1}^{2} \frac{u ^{5}}{3} d u

提出常数:

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

= 3 \cdot \frac{1}{3} \cdot \int_{1}^{2} u^{5} d u

使用幂法则

= 3 \cdot \frac{1}{3} [\frac{u ^{6}}{6}]_{1}^{2}

化简

3 \cdot \frac{1}{3} [\frac{u ^{6}}{6}]_{1}^{2} : [\frac{u ^{6}}{6}]_{1}^{2}

= [\frac{u ^{6}}{6}]_{1}^{2}

带入上下限计算后得:

\frac{21}{2}

= \frac{21}{2}

作图

流行的例子

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\int_{2}^{4} k (1 - (x - 3)^{2}) d x

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\int_{0}^{5} \frac{1}{5} x^{5} d x

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\int_{- 3}^{5} (x^{3} - 4 x) d x

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\int_{\frac{π}{2}}^{\frac{- π}{2}} ln (x) d x