Question

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

score 499 · Answer 1 · 2018-03-31 01:34:13

499

Views

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

Published on 31 Mar 2018 - 1:34

score 39 · Answer 2 · 2026-04-11 02:52:43

39

Views

Is there any reason why the limits of integration wouldn't change?

Published on 11 Apr 2026 - 2:52

score 31 · Answer 3 · 2026-04-10 21:26:17

31

Views

how to solve $\int_{-\infty}^t \sin(\omega_o(t-t'))(1+\tanh(\frac{t'}{\tau}))dt'$?

Published on 10 Apr 2026 - 21:26

score 422 · Answer 4 · 2026-04-12 05:15:45

422

Views

Using the Fourier Sine/Cosine Transform to evaluate an integral

Published on 12 Apr 2026 - 5:15

score 50 · Answer 5 · 2026-04-11 23:16:28

50

Views

Is the following definite integral necessarily zero?

Published on 11 Apr 2026 - 23:16

score 178 · Answer 6 · 2018-03-31 21:04:17

178

Views

Show that $\int_0^\pi\frac{x \sin x}{5-3\cos x}\, \mathrm dx = \frac{2 \pi \log (4/3)} 3$

Published on 31 Mar 2018 - 21:04

score 192 · Answer 7 · 2026-04-12 08:44:48

192

Views

Arrangement of definite integral in increasing order

Published on 12 Apr 2026 - 8:44

score 301 · Answer 8 · 2026-04-07 00:18:47

301

Views

Volume of revolution around $x=3$ using the disk method

Published on 07 Apr 2026 - 0:18

score 503 · Answer 9 · 2026-03-26 11:00:55

503

Views

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Published on 26 Mar 2026 - 11:00

score 130 · Answer 10 · 2026-03-26 21:27:40

130

Views

Showing $\int_{-\infty}^{\infty}\frac {\mathrm d x} {1+x+x^2}=3 \int_0^\infty \frac {\mathrm d x} {1+x+x^2}$

Published on 26 Mar 2026 - 21:27

score 91 · Answer 11 · 2018-04-01 16:13:33

91

Views

$ (a_{n})_{n\in \mathbb{N}} $ , $ a_{0}=-1 $ , $a_{n+1}=2+\int_{a_{n}}^{1} e^{-x^2}dx$

Published on 01 Apr 2018 - 16:13

score 28 · Answer 12 · 2026-04-12 08:21:45

28

Views

Orthogonality relation seems to result in an indefinite case

Published on 12 Apr 2026 - 8:21

score 695 · Answer 13 · 2026-03-26 06:25:36

695

Views

evaluating definite integrals using power series, $\sqrt{1+x^4}$

Published on 26 Mar 2026 - 6:25

score 45 · Answer 14 · 2026-04-09 00:27:42

45

Views

Two-valued change of variables for the given function

Published on 09 Apr 2026 - 0:27

score 82 · Answer 15 · 2018-04-01 22:47:29

82

Views

Integration Problem: $\frac{1}{\sqrt{2\pi}}\int^{\infty}_0\sqrt{w}e^{-w-\frac{wx^2}{2}}dw$

Published on 01 Apr 2018 - 22:47

List Question

How to evaluate $\int_0^1 \frac{1-x}{\ln x}(x+x^2+x^{2^2}+x^{2^3}+x^{2^4}+\ldots) \, dx$?

Is there any reason why the limits of integration wouldn't change?

how to solve $\int_{-\infty}^t \sin(\omega_o(t-t'))(1+\tanh(\frac{t'}{\tau}))dt'$?

Using the Fourier Sine/Cosine Transform to evaluate an integral

Is the following definite integral necessarily zero?

Show that $\int_0^\pi\frac{x \sin x}{5-3\cos x}\, \mathrm dx = \frac{2 \pi \log (4/3)} 3$

Arrangement of definite integral in increasing order

Volume of revolution around $x=3$ using the disk method

Is there a rapider or more elegant way to evaluate $\int_0^{+\infty} \frac{\cos(\pi x)\ \text{d}x}{e^{2\pi \sqrt{x}}-1}$?

Showing $\int_{-\infty}^{\infty}\frac {\mathrm d x} {1+x+x^2}=3 \int_0^\infty \frac {\mathrm d x} {1+x+x^2}$

$ (a_{n})_{n\in \mathbb{N}} $ , $ a_{0}=-1 $ , $a_{n+1}=2+\int_{a_{n}}^{1} e^{-x^2}dx$

Orthogonality relation seems to result in an indefinite case

evaluating definite integrals using power series, $\sqrt{1+x^4}$

Two-valued change of variables for the given function

Integration Problem: $\frac{1}{\sqrt{2\pi}}\int^{\infty}_0\sqrt{w}e^{-w-\frac{wx^2}{2}}dw$

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