integral from-ln(2) to ln(2) of xsinh(x)

解答

\int_{- l n (2)}^{l n (2)} x sinh (x) d x

- \frac{3}{2} + \frac{5}{2} ln (2)

十进制

0.23286 \dots

求解步骤

\int_{- l n (2)}^{l n (2)} x sinh (x) d x

使用分布积分法

= [x cosh (x) - \int cosh (x) d x]_{- l n (2)}^{l n (2)}

\int cosh (x) d x = sinh (x)

= [x cosh (x) - sinh (x)]_{- l n (2)}^{l n (2)}

带入上下限计算后得:

- \frac{3}{2} + \frac{5}{2} ln (2)

= - \frac{3}{2} + \frac{5}{2} ln (2)

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