Question

Evaluate $\int \frac {dx}{\sin \frac x2\sqrt {\cos^3 \frac x2}}$

score 1.6k · Answer 1 · 2026-04-16 18:53:53

1.6k

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Evaluate $\int \frac {dx}{\sin \frac x2\sqrt {\cos^3 \frac x2}}$

Published on 16 Apr 2026 - 18:53

score 55 · Answer 2 · 2026-04-15 02:33:10

55

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Integration by part of Gaussian r.v.

Published on 15 Apr 2026 - 2:33

score 335 · Answer 3 · 2026-04-13 18:12:31

335

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Assume that $f$ is Riemann integrable over $[a, b]$. Show that $|f| \in R[a,b]$

Published on 13 Apr 2026 - 18:12

score 72 · Answer 4 · 2026-04-16 10:54:59

72

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Can you prove, that the integral is zero or that this function is odd

Published on 16 Apr 2026 - 10:54

score 2.9k · Answer 5 · 2026-04-23 11:44:35

2.9k

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If $ f(x)= \int_0^x x^2\sin(t^2)dt$ then $f'(x)= ?$

Published on 23 Apr 2026 - 11:44

score 223 · Answer 6 · 2026-05-10 18:26:23

223

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Differential geometry - Calculating length of a curve

Published on 10 May 2026 - 18:26

score 139 · Answer 7 · 2026-05-10 23:40:20

139

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Telescoping sum involving $\int_0^\frac{\pi}{2}\cos^{2n} x\,dx$ and $\int_0^\frac{\pi}{2}x^2\cos^{2n} x\,dx$

Published on 10 May 2026 - 23:40

score 639 · Answer 8 · 2026-04-14 21:25:14

639

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why integration of $y=\frac{1}{1+x^2}$ is $\arctan(x)+c$?

Published on 14 Apr 2026 - 21:25

score 273 · Answer 9 · 2026-04-24 16:17:00

273

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Measure defined by integral is non-atomic

Published on 24 Apr 2026 - 16:17

score 37 · Answer 10 · 2026-04-14 13:20:40

37

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Does $\prod_{i=1}^N (1-f(x_i)\Delta x_i+o(\Delta x_i))\to e^{-\int_0^1f(x)dx}$ as $n\to\infty$?

Published on 14 Apr 2026 - 13:20

score 441 · Answer 11 · 2026-04-12 04:10:27

441

Views

Continuous mapping theorem with integral that depends on parameter

Published on 12 Apr 2026 - 4:10

score 55 · Answer 12 · 2026-05-11 03:19:26

55

Views

Simplify integral with random functions and their derivatives

Published on 11 May 2026 - 3:19

score 112 · Answer 13 · 2026-04-17 13:33:22

112

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what is difference between $\int_{0}^{1+x^3}\sqrt{t}$ and $\int_{0}^{x^3}\sqrt{1+t}$ and $\int_{0}^{x}\sqrt{1+t^3}$?

Published on 17 Apr 2026 - 13:33

score 88 · Answer 14 · 2026-05-04 11:10:04

88

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Evaluate $\int_{|z|=3}{\frac{9z^5}{(z-2)(1+2z)^2(1-3z)^3}}dz$

Published on 04 May 2026 - 11:10

score 108 · Answer 15 · 2026-04-17 13:57:37

108

Views

What is the closed form solution for this integral or series?

Published on 17 Apr 2026 - 13:57

List Question

Evaluate $\int \frac {dx}{\sin \frac x2\sqrt {\cos^3 \frac x2}}$

Integration by part of Gaussian r.v.

Assume that $f$ is Riemann integrable over $[a, b]$. Show that $|f| \in R[a,b]$

Can you prove, that the integral is zero or that this function is odd

If $ f(x)= \int_0^x x^2\sin(t^2)dt$ then $f'(x)= ?$

Differential geometry - Calculating length of a curve

Telescoping sum involving $\int_0^\frac{\pi}{2}\cos^{2n} x\,dx$ and $\int_0^\frac{\pi}{2}x^2\cos^{2n} x\,dx$

why integration of $y=\frac{1}{1+x^2}$ is $\arctan(x)+c$?

Measure defined by integral is non-atomic

Does $\prod_{i=1}^N (1-f(x_i)\Delta x_i+o(\Delta x_i))\to e^{-\int_0^1f(x)dx}$ as $n\to\infty$?

Continuous mapping theorem with integral that depends on parameter

Simplify integral with random functions and their derivatives

what is difference between $\int_{0}^{1+x^3}\sqrt{t}$ and $\int_{0}^{x^3}\sqrt{1+t}$ and $\int_{0}^{x}\sqrt{1+t^3}$?

Evaluate $\int_{|z|=3}{\frac{9z^5}{(z-2)(1+2z)^2(1-3z)^3}}dz$

What is the closed form solution for this integral or series?

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