Question

Closed form of integral: $\displaystyle\int_{1}^{\infty}\frac{ax-b+1}{x^{\frac{1}{b}}}e^{-\frac{a}{b}x}\ln\left(ax-b+1\right)\mathrm{d}x$

score 460 · Answer 1 · 2026-04-16 14:41:55

460

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Closed form of integral: $\displaystyle\int_{1}^{\infty}\frac{ax-b+1}{x^{\frac{1}{b}}}e^{-\frac{a}{b}x}\ln\left(ax-b+1\right)\mathrm{d}x$

Published on 16 Apr 2026 - 14:41

score 107 · Answer 2 · 2026-04-12 19:50:24

107

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How do I perform following integral or find out for what values of parameters $c,\phi$ it is positive and for what values it is negative?

Published on 12 Apr 2026 - 19:50

score 183 · Answer 3 · 2026-04-15 13:54:01

183

Views

Definite integral $\int_{0}^{\infty} \frac{dx}{(1+e^{ax})(1+e^{x/a})}$

Published on 15 Apr 2026 - 13:54

score 28 · Answer 4 · 2026-04-14 15:42:57

28

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Riemann series theorem for integrals

Published on 14 Apr 2026 - 15:42

score 164 · Answer 5 · 2026-03-25 02:34:59

164

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Is there a simple way to evaluate $\int_0^1 \arctan x \ln \left(\frac{1-x}{1+x}\right) d x?$

Published on 25 Mar 2026 - 2:34

score 169 · Answer 6 · 2026-04-16 04:58:34

169

Views

Why are the improper integrals $\int_{-\infty}^{\infty}x\,\mathrm{d}x$ and $\lim\limits_{n\to\infty} \int_{-n}^{n}x\,\mathrm{d}x$ different?

Published on 16 Apr 2026 - 4:58

score 120 · Answer 7 · 2026-04-16 18:42:43

120

Views

Checking convergence/ divergence of $\int_1^\infty \frac{\log{x}}{x^2}\,dx$

Published on 16 Apr 2026 - 18:42

score 765 · Answer 8 · 2026-04-14 20:44:42

765

Views

How to evaluate $\displaystyle\int_{-\infty}^{\infty}e^{-\frac{x^{2}}{2}}\ln\left(1+e^{x}\right)\mathrm{d}x\textbf{ efficiently}$?

Published on 14 Apr 2026 - 20:44

score 94 · Answer 9 · 2026-04-11 03:19:32

94

Views

Can improper integral from minus infinity to postive infinity be defined as double limit?

Published on 11 Apr 2026 - 3:19

score 53 · Answer 10 · 2026-04-16 04:11:30

53

Views

How to approach this integral? $ \int_0^\Theta {\frac{1}{a+b\cot\left({\pi{x}^c}\right)}} dx $

Published on 16 Apr 2026 - 4:11

score 129 · Answer 11 · 2026-04-16 11:24:10

129

Views

Limit $\lim _{t\to \infty} \int_t^\infty t \frac {\sin^2 (u)}{u^2} du$

Published on 16 Apr 2026 - 11:24

score 579 · Answer 12 · 2026-04-17 09:51:28

579

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Evaulate $\int_{-\infty}^{\infty} \frac{\ln(x^2+1)}{x^4+x^2+1}dx$

Published on 17 Apr 2026 - 9:51

score 426 · Answer 13 · 2026-04-15 02:24:05

426

Views

Calculating $\;\int_{-\infty}^{\infty}\frac{1}{(e^x-1-x)^2+4\pi^2}~dx$

Published on 15 Apr 2026 - 2:24

score 37 · Answer 14 · 2026-04-11 14:50:12

37

Views

Asymptotic analysis of an integral - continuous time random walk framework

Published on 11 Apr 2026 - 14:50

score 53 · Answer 15 · 2026-04-09 05:24:48

53

Views

Dealing with indefinite integrals when using Least Squares Estimation

Published on 09 Apr 2026 - 5:24

List Question

Closed form of integral: $\displaystyle\int_{1}^{\infty}\frac{ax-b+1}{x^{\frac{1}{b}}}e^{-\frac{a}{b}x}\ln\left(ax-b+1\right)\mathrm{d}x$

How do I perform following integral or find out for what values of parameters $c,\phi$ it is positive and for what values it is negative?

Definite integral $\int_{0}^{\infty} \frac{dx}{(1+e^{ax})(1+e^{x/a})}$

Riemann series theorem for integrals

Is there a simple way to evaluate $\int_0^1 \arctan x \ln \left(\frac{1-x}{1+x}\right) d x?$

Why are the improper integrals $\int_{-\infty}^{\infty}x\,\mathrm{d}x$ and $\lim\limits_{n\to\infty} \int_{-n}^{n}x\,\mathrm{d}x$ different?

Checking convergence/ divergence of $\int_1^\infty \frac{\log{x}}{x^2}\,dx$

How to evaluate $\displaystyle\int_{-\infty}^{\infty}e^{-\frac{x^{2}}{2}}\ln\left(1+e^{x}\right)\mathrm{d}x\textbf{ efficiently}$?

Can improper integral from minus infinity to postive infinity be defined as double limit?

How to approach this integral? $ \int_0^\Theta {\frac{1}{a+b\cot\left({\pi{x}^c}\right)}} dx $

Limit $\lim _{t\to \infty} \int_t^\infty t \frac {\sin^2 (u)}{u^2} du$

Evaulate $\int_{-\infty}^{\infty} \frac{\ln(x^2+1)}{x^4+x^2+1}dx$

Calculating $\;\int_{-\infty}^{\infty}\frac{1}{(e^x-1-x)^2+4\pi^2}~dx$

Asymptotic analysis of an integral - continuous time random walk framework

Dealing with indefinite integrals when using Least Squares Estimation

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