Solve $ \lim_{n \rightarrow +\infty}\int_0^1 \frac{dx}{1+x^n}=$ :
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举一反三
- Solve $ \lim_{x \rightarrow \infty}[x-x^2\ln{(1+\frac{1}{x}})]=$ :<br/>______
- 下面积分收敛的是 A: $\int_0^\infty \frac{x^{4/3}}{1+x^2} dx$ B: $\int_1^\infty \frac{dx}{x \sqrt[3]{1+x^3}}$ C: $\int_1^\infty \frac{1}{x} dx$ D: $\int_1^\infty \frac{\arctan x}{x} dx$
- Solve $n \in \mathbb{N}, \int_0^{\frac{\pi}{2}}(\sin^n{x}-\cos^n{x})dx=$ :<br/>______
- Solve $ \frac{1}{\pi}\int_0^{\frac{\pi}{2}}\sin^4{x}dx=$ :<br/>______
- Solve $\sum_{n=1}^{\infty}\frac{1}{n(n+1)(n+2)}$:<br/>______