Question

Difficult logarithmic integral: $\int_0^\Lambda r^{d - 1}\log(1 + a\sqrt{r^2 + m_1^2} + b\sqrt{r^2 + m_2^2}) dr$

score 287 · Answer 1 · 2026-04-16 23:18:31

287

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Difficult logarithmic integral: $\int_0^\Lambda r^{d - 1}\log(1 + a\sqrt{r^2 + m_1^2} + b\sqrt{r^2 + m_2^2}) dr$

Published on 16 Apr 2026 - 23:18

score 98 · Answer 2 · 2026-04-08 22:46:32

98

Views

Suggestions on the integration of Dirac $\delta$-function

Published on 08 Apr 2026 - 22:46

score 79 · Answer 3 · 2026-04-15 22:35:50

79

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Calculate $\int\frac{a}{\sin(x)\sqrt{\sin^2(x)-a^2}}dx$

Published on 15 Apr 2026 - 22:35

score 68 · Answer 4 · 2026-04-12 17:08:50

68

Views

Linking definite and indefinite integral

Published on 12 Apr 2026 - 17:08

score 63 · Answer 5 · 2026-04-16 06:11:05

63

Views

Calculate the line intergal: $A=\int_C \sqrt{x^2+y^2}ds$

Published on 16 Apr 2026 - 6:11

score 93 · Answer 6 · 2026-04-08 18:19:54

93

Views

How can I quickly perform substitutions in integration?

Published on 08 Apr 2026 - 18:19

score 107 · Answer 7 · 2026-04-15 02:54:35

107

Views

High school indefinite integration question: $\int 1/(x^2+6x+5)dx $ but must complete the square then use a trigonometric substitution.

Published on 15 Apr 2026 - 2:54

score 143 · Answer 8 · 2026-04-17 01:30:50

143

Views

Find $ \int \frac{\sec x(2+\sec x)}{(1+2\sec x)^2}\,dx$

Published on 17 Apr 2026 - 1:30

score 75 · Answer 9 · 2026-04-17 08:02:22

75

Views

Given that $\int \frac{1}{x\sqrt{x^2-1}}dx=\arccos(\frac{1}{x})+C$, what is $\int\frac{1}{x\sqrt{x^2-a^2}}dx$?

Published on 17 Apr 2026 - 8:02

score 45 · Answer 10 · 2026-05-05 18:52:59

45

Views

Orthogonality between derivative and integral of a periodic signal

Published on 05 May 2026 - 18:52

score 89 · Answer 11 · 2026-04-16 09:05:40

89

Views

Integral of exponential times $\frac{x^2}{x^2+a}$

Published on 16 Apr 2026 - 9:05

score 130 · Answer 12 · 2026-04-14 02:32:35

130

Views

can $\int_{0}^{\infty} (f(z)^n+f(z)^{n+1})$ grow forever?

Published on 14 Apr 2026 - 2:32

score 70 · Answer 13 · 2026-04-14 07:32:31

70

Views

Does $\int_{0}^{\infty} f(x)^n dx$ always shrink?

Published on 14 Apr 2026 - 7:32

score 37 · Answer 14 · 2026-04-17 00:24:36

37

Views

Compute $\int dq \ q^{n} j_{\ell} \left( q r \right) j_{\ell}\left( q R \right)$

Published on 17 Apr 2026 - 0:24

score 61 · Answer 15 · 2026-04-15 16:32:24

61

Views

Can substitutions in indefinite integral make it non elementary?

Published on 15 Apr 2026 - 16:32

List Question

Difficult logarithmic integral: $\int_0^\Lambda r^{d - 1}\log(1 + a\sqrt{r^2 + m_1^2} + b\sqrt{r^2 + m_2^2}) dr$

Suggestions on the integration of Dirac $\delta$-function

Calculate $\int\frac{a}{\sin(x)\sqrt{\sin^2(x)-a^2}}dx$

Linking definite and indefinite integral

Calculate the line intergal: $A=\int_C \sqrt{x^2+y^2}ds$

How can I quickly perform substitutions in integration?

High school indefinite integration question: $\int 1/(x^2+6x+5)dx $ but must complete the square then use a trigonometric substitution.

Find $ \int \frac{\sec x(2+\sec x)}{(1+2\sec x)^2}\,dx$

Given that $\int \frac{1}{x\sqrt{x^2-1}}dx=\arccos(\frac{1}{x})+C$, what is $\int\frac{1}{x\sqrt{x^2-a^2}}dx$?

Orthogonality between derivative and integral of a periodic signal

Integral of exponential times $\frac{x^2}{x^2+a}$

can $\int_{0}^{\infty} (f(z)^n+f(z)^{n+1})$ grow forever?

Does $\int_{0}^{\infty} f(x)^n dx$ always shrink?

Compute $\int dq \ q^{n} j_{\ell} \left( q r \right) j_{\ell}\left( q R \right)$

Can substitutions in indefinite integral make it non elementary?

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