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

解答

\int_{0}^{l n (2)} e^{x} (1 + e^{x})^{3} d x

\frac{65}{4}

十进制

16.25

求解步骤

\int_{0}^{l n (2)} e^{x} (1 + e^{x})^{3} d x

使用换元积分法

= \int_{2}^{3} u^{3} d u

使用幂法则

= [\frac{u ^{4}}{4}]_{2}^{3}

带入上下限计算后得:

\frac{65}{4}

= \frac{65}{4}

\int_{0}^{1} 5 x^{4} (5 - x^{5}) d x

\int_{- 2}^{1} (2 - y^{2}) - (3 + y^{2}) d y

\int_{1}^{5} 4 \frac{( x - 1 ) ^{3}}{x ^{2}} d x

\int_{2}^{e + 1} \frac{x}{x + 1} d x

\int_{- 5}^{0} 3 + 25 - x^{2} d x