List questions from substitution

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Understanding Variable of Integration

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Find the limit $ \lim_{x \to (\frac{1}{2})^{-}} \frac{\ln(1 - 2x)}{\tan \pi x} $

Published on 19 Jul 2017 - 12:39

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Probability mapping from lower to higher dimension with noise

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If $\frac{\sin(x)}{a}=\frac{\cos(x)}{b}$ then $a\sin(2x)+b\cos(2x)=?$

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Integrate $\int t^{-\frac{1}{2}} e^{-\frac{c^2}{4t}} \, \mathrm{d}t$

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Solving trigonometric equations

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Solving the the Integral: $\int\frac{1}{u^2-2}du$

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Solving the the Integral: $\int\frac{\ln(x+3)}{(x+3)^{\frac{1}{3}}}dx$

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show that $xyz(x-y)(x-z)(y-z)\le 27$

Published on 26 Mar 2026 - 12:48

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Substitution Question

Published on 30 Mar 2026 - 3:52

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Degree of $\mathbb{Q}(\sqrt{1 + \sqrt{2}})$ over $\mathbb{Q}$

Published on 30 Jul 2017 - 19:01

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Substitution of Lebesgue Stieltjes integral

Published on 31 Jul 2017 - 14:42

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Inequality $\frac{x_1^2}{x_1^2+x_2x_3}+\frac{x_2^2}{x_2^2+x_3x_4}+\cdots+\frac{x_{n-1}^2}{x_{n-1}^2+x_nx_1}+\frac{x_n^2}{x_n^2+x_1x_2}\le n-1$

Published on 01 Aug 2017 - 17:53

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If $ x \in \left(0,\frac{\pi}{2}\right)$. Then value of $x$ in $ \frac{3}{\sqrt{2}}\sec x-\sqrt{2}\csc x = 1$

Published on 02 Aug 2017 - 4:29

List Question

Integration by substitution

Understanding Variable of Integration

Find the limit $ \lim_{x \to (\frac{1}{2})^{-}} \frac{\ln(1 - 2x)}{\tan \pi x} $

Probability mapping from lower to higher dimension with noise

If $\frac{\sin(x)}{a}=\frac{\cos(x)}{b}$ then $a\sin(2x)+b\cos(2x)=?$

Integrate $\int t^{-\frac{1}{2}} e^{-\frac{c^2}{4t}} \, \mathrm{d}t$

Solving trigonometric equations

Solving the the Integral: $\int\frac{1}{u^2-2}du$

Solving the the Integral: $\int\frac{\ln(x+3)}{(x+3)^{\frac{1}{3}}}dx$

show that $xyz(x-y)(x-z)(y-z)\le 27$

Substitution Question

Degree of $\mathbb{Q}(\sqrt{1 + \sqrt{2}})$ over $\mathbb{Q}$

Substitution of Lebesgue Stieltjes integral

Inequality $\frac{x_1^2}{x_1^2+x_2x_3}+\frac{x_2^2}{x_2^2+x_3x_4}+\cdots+\frac{x_{n-1}^2}{x_{n-1}^2+x_nx_1}+\frac{x_n^2}{x_n^2+x_1x_2}\le n-1$

If $ x \in \left(0,\frac{\pi}{2}\right)$. Then value of $x$ in $ \frac{3}{\sqrt{2}}\sec x-\sqrt{2}\csc x = 1$

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