Posted by haifeng on 2026-05-10 18:31:36 last update 2026-05-10 18:31:36 | Answers (0) | 收藏
求积分 $\displaystyle\int_{0}^{+\infty}\frac{1}{(1+x^2)^{\frac{3}{2}}}\mathrm{d}x$.
Posted by haifeng on 2023-03-25 14:10:45 last update 2023-03-25 14:11:06 | Answers (2) | 收藏
计算定积分 $\displaystyle\int_0^{\infty}\frac{x\ln x}{(1+x^2)^2}\mathrm{d}x$.
Posted by haifeng on 2022-12-15 08:39:42 last update 2022-12-15 08:43:03 | Answers (1) | 收藏
若
\[\int_a^{+\infty}\frac{\mathrm{d}x}{e^{x+1}+e^{3-x}}=\frac{\pi}{4e^2},\]
求常数 $a$.
[Hint] 被积函数分子分母同乘以 $e^x$, 然后换元. 答案 $a=1$.