6 Computing the integral $x^2\textrm{sech}^2(x)$ 6 Find : $\lim_{n\to\infty}\sum_{k=0}^n\frac{\binom{n}{k}}{n^k(k+1)}$ 6 Evaluating $\int\limits_0^\infty \mathcal{e}^{-x}\ln^{2}x\,dx$ 6 Taylor approximation of cos function 5 Problem with value of integral

Reputation (6,161)

 +30 Closed form of $\int_{0}^{1}\int_{0}^{1}\frac{1}{1-\frac{xy}{2}}dxdy$ +30 How do you integrate $\int_{0}^{\infty}\frac{a\cos{(cx)}}{a^2+x^2}dx$? +5 Integral $\int_0^1 \sqrt{\frac{x^2-2}{x^2-1}}\, dx=\frac{\pi\sqrt{2\pi}}{\Gamma^2(1/4)}+\frac{\Gamma^2(1/4)}{4\sqrt{2\pi}}$ +5 concerning the coefficients of $P_n(x)=(x-1)(x-2)\cdots (x-n)$

Questions (120)

 21 Freaky dots in the complex plane 16 $\int_{-\infty}^{\infty}\frac{\mathrm{d}x}{ax^2+bx+c}=\pi$ similar identities 15 Integral $T_n=\int_{0}^{\pi/2}x^{n}\ln(1+\tan x)\,dx$ 14 Evaluate $\int_{-\pi/4}^{\pi/4}\frac{x}{\sin x}\mathrm{d}x$ 14 Relationship between Catalan's constant and $\pi$

Tags (128)

 196 integration × 233 30 real-analysis × 39 126 calculus × 132 29 indefinite-integrals × 32 85 definite-integrals × 80 21 improper-integrals × 17 32 sequences-and-series × 65 16 derivatives × 24 31 trigonometry × 30 13 algebra-precalculus × 15

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