Question

Integration by substitution: use of appropriate substitutions with roots of even index

score 166 · Answer 1 · 2022-03-27 18:55:28

166

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Integration by substitution: use of appropriate substitutions with roots of even index

Published on 27 Mar 2022 - 18:55

score 79 · Answer 2 · 2022-04-01 11:52:37

79

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Effective method to solve $\frac{\sqrt[3]{1+x} -\sqrt[3]{1-x}}{\sqrt[3]{1+x} +\sqrt[3]{1-x}} = \frac{x(x^2+3)}{3x^2+1} $

Published on 01 Apr 2022 - 11:52

score 78 · Answer 3 · 2026-03-27 10:09:42

78

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Evaluating $\int_{1/\sqrt{2}}^1\frac{1}{(3y^2-1)\sqrt{2y^2-1}}\,\mathrm{d}y$; how do you avoid using a complex substitution?

Published on 27 Mar 2026 - 10:09

score 71 · Answer 4 · 2022-04-14 16:24:00

71

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How and why does this variable substitution in this integral work?

Published on 14 Apr 2022 - 16:24

score 94 · Answer 5 · 2022-04-15 04:00:20

94

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Help evaluating a limit.

Published on 15 Apr 2022 - 4:00

score 710 · Answer 6 · 2022-04-16 11:30:53

710

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I have the integral $\int_{-1}^{1} \frac{\arccos(x)}{1+x^2} \,dx $ and some questions. Any help appreciated!

Published on 16 Apr 2022 - 11:30

score 59 · Answer 7 · 2022-04-18 19:44:27

59

Views

U substitution to turn a double integral into a convolution?

Published on 18 Apr 2022 - 19:44

score 166 · Answer 8 · 2022-04-21 00:32:55

166

Views

How to select a choice of $u$ to solve $\int \frac{x^2}{1+x^2} dx$ by substitution?

Published on 21 Apr 2022 - 0:32

score 65 · Answer 9 · 2022-04-22 06:41:15

65

Views

Does Euler Third Substitution gives different answers?

Published on 22 Apr 2022 - 6:41

score 44 · Answer 10 · 2022-04-22 18:10:52

44

Views

Area under curve in two different ways

Published on 22 Apr 2022 - 18:10

score 41 · Answer 11 · 2022-04-29 11:39:09

41

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Converse of renaming substitutions

Published on 29 Apr 2022 - 11:39

score 213 · Answer 12 · 2022-05-02 11:04:50

213

Views

Convergence of improper integral, $\cos(1/x)$

Published on 02 May 2022 - 11:04

score 74 · Answer 13 · 2022-05-03 16:02:55

74

Views

Substitution in 2 variable limits

Published on 03 May 2022 - 16:02

score 48 · Answer 14 · 2026-04-02 16:01:19

48

Views

Difficulty understanding the substitution $dS(y)=rdS(z)$

Published on 02 Apr 2026 - 16:01

score 82 · Answer 15 · 2022-05-10 10:24:11

82

Views

Show equality between these two series

Published on 10 May 2022 - 10:24

List Question

Integration by substitution: use of appropriate substitutions with roots of even index

Effective method to solve $\frac{\sqrt[3]{1+x} -\sqrt[3]{1-x}}{\sqrt[3]{1+x} +\sqrt[3]{1-x}} = \frac{x(x^2+3)}{3x^2+1} $

Evaluating $\int_{1/\sqrt{2}}^1\frac{1}{(3y^2-1)\sqrt{2y^2-1}}\,\mathrm{d}y$; how do you avoid using a complex substitution?

How and why does this variable substitution in this integral work?

Help evaluating a limit.

I have the integral $\int_{-1}^{1} \frac{\arccos(x)}{1+x^2} \,dx $ and some questions. Any help appreciated!

U substitution to turn a double integral into a convolution?

How to select a choice of $u$ to solve $\int \frac{x^2}{1+x^2} dx$ by substitution?

Does Euler Third Substitution gives different answers?

Area under curve in two different ways

Converse of renaming substitutions

Convergence of improper integral, $\cos(1/x)$

Substitution in 2 variable limits

Difficulty understanding the substitution $dS(y)=rdS(z)$

Show equality between these two series

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