Martin Gales
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 17 Integrate square of the log-sine integral: $\int_0^{\frac{\pi}{2}}\ln^{2}(\sin(x))dx$ 14 Evaluating $\int_{0}^{\infty} \frac{x^{3}- \sin^{3}(x)}{x^{5}} \ dx$ using contour integration 12 Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ 11 Prove that $\int_0^{\infty} \frac{\sin(2013 x)}{x(\cos x+\cosh x)}dx=\frac{\pi}{4}$ 8 Prove that a non-zero acceleration is perpendicular to a constant speed

### Reputation (2,835)

 +10 Ways to evaluate $\int \sec \theta \, \mathrm d \theta$ +31 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis +10 Prove that $\int_0^{+\infty} \frac{\ln x}{a^2+x^2} dx = \frac{\pi\ln a}{2a}$ +5 Find $\lim \limits_{y\rightarrow\infty}\left (\ln^2y\,-2\int_{0}^y\frac{\ln x}{\sqrt{x^2+1}}dx\right)$

### Questions (22)

 65 Calculating the integral $\int_{0}^{\infty} \frac{\cos x}{1+x^2}\mathrm{d}x$ without using complex analysis 32 Evaluating $\int_{0}^{1}\frac{1-x}{1+x}\frac{\mathrm dx}{\ln x}$ 19 Integral $\int_{0}^1\frac{\ln\frac{3+x}{3-x}}{\sqrt{x(1-x)}}dx$ 17 Evaluating $\int_{0}^{\infty}\sin^3(x)\cos[a\tan(x)]\frac{dx}{x}$ 15 How many trees in a forest?

### Tags (33)

 114 integration × 41 22 contour-integration × 3 78 calculus × 22 21 improper-integrals × 9 50 definite-integrals × 15 19 real-analysis × 9 29 trigonometry × 7 14 sequences-and-series × 12 23 complex-analysis × 6 14 indefinite-integrals × 2

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 Mathematics 2,835 rep 11529