List questions from substitution

Published on 29 Mar 2026 - 4:09

130

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For $a, b, c$ is the length of three sides of a triangle. Prove that $\left|\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}\right|<\frac{1}{8}$

Published on 25 Mar 2026 - 17:26

1.8k

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Justification for indefinite integration by substitution

Published on 24 Feb 2017 - 16:55

195

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Showing that $\int \frac {dx}{\sqrt{x^2+a^2}} \;=\; \ln\,\biggl| x+\sqrt{x^2+a^2}\,\biggr| +C$

Published on 25 Feb 2017 - 16:20

27

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Is it ok to get different solutions if I use different substitutions? (Homogenous ODE)

Published on 25 Feb 2017 - 23:35

99

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Unsure why this improper integral converges at 2.

Published on 26 Feb 2017 - 0:20

137

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Indefinite integral $\int \frac{2^x}{2^{2x}-4}dx$

Published on 26 Feb 2017 - 2:18

882

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integrate $2\int _0^2\:r^2\sqrt{(1-(r-1)^2)} dr$

Published on 28 Feb 2017 - 10:47

75

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I need help on understanding an integral substitution

Published on 28 Feb 2017 - 15:28

231

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$\int \sec^3x dx$ in disguise

Published on 25 Mar 2026 - 22:09

189

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Help with understanding this u-substitution that makes no sense to me

Published on 27 Mar 2026 - 0:04

240

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Prove that $\frac{1}{\left(2a+b\right)^2}+\frac{1}{\left(2b+c\right)^2}+\frac{1}{\left(2c+a\right)^2}\ge\frac{1}{ab+bc+ca}$

Published on 25 Mar 2026 - 22:05

110

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Tricky Trig Substitution

Published on 25 Mar 2026 - 20:27

434

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Finding slope of tangent line to $y = 2\sin^2(4x) + 3\cos^2(2x)$ at the point $x_0 = \frac{10\pi}{3}$

Published on 25 Mar 2026 - 21:51

404

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Find $\int^r_{-r} \sqrt{r^2 - x^2} \:dx$ where r is a positive constant.

Published on 05 Mar 2017 - 20:11

List Question

Tricky inequality involving 3 variables

For $a, b, c$ is the length of three sides of a triangle. Prove that $\left|\frac{a-b}{a+b}+\frac{b-c}{b+c}+\frac{c-a}{c+a}\right|<\frac{1}{8}$

Justification for indefinite integration by substitution

Showing that $\int \frac {dx}{\sqrt{x^2+a^2}} \;=\; \ln\,\biggl| x+\sqrt{x^2+a^2}\,\biggr| +C$

Is it ok to get different solutions if I use different substitutions? (Homogenous ODE)

Unsure why this improper integral converges at 2.

Indefinite integral $\int \frac{2^x}{2^{2x}-4}dx$

integrate $2\int _0^2\:r^2\sqrt{(1-(r-1)^2)} dr$

I need help on understanding an integral substitution

$\int \sec^3x dx$ in disguise

Help with understanding this u-substitution that makes no sense to me

Prove that $\frac{1}{\left(2a+b\right)^2}+\frac{1}{\left(2b+c\right)^2}+\frac{1}{\left(2c+a\right)^2}\ge\frac{1}{ab+bc+ca}$

Tricky Trig Substitution

Finding slope of tangent line to $y = 2\sin^2(4x) + 3\cos^2(2x)$ at the point $x_0 = \frac{10\pi}{3}$

Find $\int^r_{-r} \sqrt{r^2 - x^2} \:dx$ where r is a positive constant.

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