Question

How to integrate: $\int \frac{1+\sqrt{x+1}}{1-\sqrt{x+1}}dx$

score 88 · Answer 1 · 2023-02-07 11:41:36

88

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How to integrate: $\int \frac{1+\sqrt{x+1}}{1-\sqrt{x+1}}dx$

Published on 07 Feb 2023 - 11:41

score 76 · Answer 2 · 2023-02-10 09:26:08

76

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Proving an example of the Substitution Rule Rigorously

Published on 10 Feb 2023 - 9:26

score 67 · Answer 3 · 2023-02-14 23:30:47

67

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Hints to solve an equation containing $\int\frac{dx}{x\sqrt{(1+x^{-4})^n-1}}$ for $n<0$

Published on 14 Feb 2023 - 23:30

score 90 · Answer 4 · 2023-02-17 16:57:39

90

Views

Strategy for integrating product of powers and trigonometric functions

Published on 17 Feb 2023 - 16:57

score 120 · Answer 5 · 2023-02-19 22:12:07

120

Views

Expressing the integral of a quartic polynomial as an elliptic integral of first kind.

Published on 19 Feb 2023 - 22:12

score 28 · Answer 6 · 2023-02-20 16:03:07

28

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$P := \{x ∈\mathbb{R}^3 : x_3 = x_1^2 + x_2^2 < 4\}$ . Sketch $P$ and calculate its surface area.

Published on 20 Feb 2023 - 16:03

score 34 · Answer 7 · 2023-02-21 16:10:10

34

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Calculate $\int_{A}(x + y)^{1/3} (x − y)^{1/2} dλ_2(x, y)$ using substitution

Published on 21 Feb 2023 - 16:10

score 70 · Answer 8 · 2023-02-22 19:40:40

70

Views

Bijective mapping/substitution - proof?

Published on 22 Feb 2023 - 19:40

score 123 · Answer 9 · 2023-02-22 23:30:49

123

Views

$\int \frac{x^2}{\sqrt{5-x^2}}dx$ using substitution $u = \sqrt{5-x^2}$?

Published on 22 Feb 2023 - 23:30

score 86 · Answer 10 · 2023-02-23 18:37:12

86

Views

Possible shortcut to integrate the double integral $\iint \frac{1}{x^2+y^2-2x+6y+20} dA$ over a region

Published on 23 Feb 2023 - 18:37

score 61 · Answer 11 · 2023-02-25 20:53:06

61

Views

How do you solve $y'' + 4x =0$ using $p=y'$ and $p(\mathrm dp/\mathrm dy) = y''\;?$

Published on 25 Feb 2023 - 20:53

score 85 · Answer 12 · 2023-02-26 21:11:48

85

Views

How do you solve $y''+4y=0$ using $='$ and $(d/d)=''$?

Published on 26 Feb 2023 - 21:11

score 118 · Answer 13 · 2023-03-02 11:42:09

118

Views

Why does $\frac{dx}{\cos x}$ cancel out in this integration by substitution

Published on 02 Mar 2023 - 11:42

score 40 · Answer 14 · 2023-03-04 10:03:57

40

Views

dot product of displacement vector with gradient

Published on 04 Mar 2023 - 10:03

score 107 · Answer 15 · 2023-03-05 23:53:58

107

Views

Connection between Integration by substitution and Line integral

Published on 05 Mar 2023 - 23:53

List Question

How to integrate: $\int \frac{1+\sqrt{x+1}}{1-\sqrt{x+1}}dx$

Proving an example of the Substitution Rule Rigorously

Hints to solve an equation containing $\int\frac{dx}{x\sqrt{(1+x^{-4})^n-1}}$ for $n<0$

Strategy for integrating product of powers and trigonometric functions

Expressing the integral of a quartic polynomial as an elliptic integral of first kind.

$P := \{x ∈\mathbb{R}^3 : x_3 = x_1^2 + x_2^2 < 4\}$ . Sketch $P$ and calculate its surface area.

Calculate $\int_{A}(x + y)^{1/3} (x − y)^{1/2} dλ_2(x, y)$ using substitution

Bijective mapping/substitution - proof?

$\int \frac{x^2}{\sqrt{5-x^2}}dx$ using substitution $u = \sqrt{5-x^2}$?

Possible shortcut to integrate the double integral $\iint \frac{1}{x^2+y^2-2x+6y+20} dA$ over a region

How do you solve $y'' + 4x =0$ using $p=y'$ and $p(\mathrm dp/\mathrm dy) = y''\;?$

How do you solve $y''+4y=0$ using $='$ and $(d/d)=''$?

Why does $\frac{dx}{\cos x}$ cancel out in this integration by substitution

dot product of displacement vector with gradient

Connection between Integration by substitution and Line integral

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