# experimentX

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 14 Calculus proof for the area of a circle 12 How to compute $\sqrt{i + 1}$ 9 What's the formula of this sequence? 8 How prove this inequality 8 Showing that $\int_{0}^{\pi/2}\frac{1}{\sqrt{\sin{x}}}\;{dx}=\int_{0}^{\pi/2}\frac{2}{\sqrt{2-\sin^2{x}}}\;{dx}?$

# 4,972 Reputation

 +20 How to prove that $\lim\limits_{x\to0}\frac{\sin x}x=1$? +5 how to evaluate $\int_0^\infty e^{- \left ( x - \frac a x \right )^2} dx$ +10 Show that $\int \limits_{0}^{\infty}\frac{x}{\sinh ax}dx=\left(\frac{\pi}{2a}\right)^2$ +15 Where is the error in this integration example?

# 44 Questions

 18 Evaluate:: $2 \sum_{n=1}^\infty \frac{(-1)^{n+1}}{n+1}\left( 1 + \frac12 +\cdots + \frac 1n\right)$ 10 How to solve an exponential equation with two different bases: $3^x - 2^x = 5$ 8 Evaluate: $\sum_{n=1}^{\infty}\frac{1}{n k^n}$ 8 Evaluate: $\int_{0}^\infty e^{-x^2} \cos^n(x) dx$ 8 how to evaluate $\int_0^\infty e^{- \left ( x - \frac a x \right )^2} dx$

# 76 Tags

 95 calculus × 48 32 real-analysis × 20 68 integration × 33 24 inequality × 7 67 limit × 27 18 complex-numbers × 4 58 sequences-and-series × 20 16 summation × 7 43 homework × 37 15 complex-analysis × 8

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 Stack Overflow 7,010 rep 33674 Mathematics 4,972 rep 926 Ask Ubuntu 495 rep 1822 Physics 399 rep 316 Mathematica 245 rep 27