Question

Evaluate $\int_0^1 \log^n(x^a)\log^m(1-x^{\color{red}{\alpha}})x^b(1-x^{\color{red}{\beta}})^t\mathrm dx$ with $\alpha\ne\beta$

score 278 · Answer 1 · 2026-03-25 10:24:53

278

Views

Evaluate $\int_0^1 \log^n(x^a)\log^m(1-x^{\color{red}{\alpha}})x^b(1-x^{\color{red}{\beta}})^t\mathrm dx$ with $\alpha\ne\beta$

Published on 25 Mar 2026 - 10:24

score 229 · Answer 2 · 2018-10-20 18:03:45

229

Views

Evaluate $\int{ \ln(\sqrt{x})dx}$ using integration by parts

Published on 20 Oct 2018 - 18:03

score 418 · Answer 3 · 2018-10-20 18:07:45

418

Views

Solving Problems of the Type $\log(x) = ax^2 + bx + c$

Published on 20 Oct 2018 - 18:07

score 274 · Answer 4 · 2026-03-28 09:33:45

274

Views

Confusion regarding Powers of Quotients Property and Change of Base Formula of Logs

Published on 28 Mar 2026 - 9:33

score 109 · Answer 5 · 2018-10-21 20:51:07

109

Views

Why $\log(x+1)=\log(1+\frac{1}{x})+\log(x)$?

Published on 21 Oct 2018 - 20:51

score 94 · Answer 6 · 2018-10-22 13:22:19

94

Views

How do you show that $\sum_{n=1}^{\infty}(-1)^{n}\dfrac{3n-1}{n^2 + n} = \log\left({32}\right) - 4$?

Published on 22 Oct 2018 - 13:22

score 41 · Answer 7 · 2018-10-22 16:58:31

41

Views

Natural Logarithm contradiction?

Published on 22 Oct 2018 - 16:58

score 28 · Answer 8 · 2018-10-22 21:16:58

28

Views

When is x +/- and when is it just positive when solving logarithms

Published on 22 Oct 2018 - 21:16

score 81 · Answer 9 · 2018-10-23 08:31:34

81

Views

Proving that $f(x) = \log(1 +x^2)$ is less than $|f'(x)|$ in a small neighbourhood around $0$

Published on 23 Oct 2018 - 8:31

score 25 · Answer 10 · 2018-10-23 14:16:18

25

Views

Basic Combinatorial Probability with Dice

Published on 23 Oct 2018 - 14:16

score 149 · Answer 11 · 2026-03-26 11:00:18

149

Views

Comparing expectations of logarithms of the random variables

Published on 26 Mar 2026 - 11:00

score 83 · Answer 12 · 2026-03-30 23:19:50

83

Views

Inequality with logarithm, missing one zero

Published on 30 Mar 2026 - 23:19

score 927 · Answer 13 · 2026-03-25 15:49:11

927

Views

Comparing logarithms with different bases

Published on 25 Mar 2026 - 15:49

score 3.9k · Answer 14 · 2018-10-24 00:07:10

3.9k

Views

What is the one-to-one property and why does it work for logarithms?

Published on 24 Oct 2018 - 0:07

score 94 · Answer 15 · 2026-03-25 06:06:23

94

Views

A very strict inequality for $\ln n$ and $H_{n-1}$, with $n>2$, searching for proof

Published on 25 Mar 2026 - 6:06

List Question

Evaluate $\int_0^1 \log^n(x^a)\log^m(1-x^{\color{red}{\alpha}})x^b(1-x^{\color{red}{\beta}})^t\mathrm dx$ with $\alpha\ne\beta$

Evaluate $\int{ \ln(\sqrt{x})dx}$ using integration by parts

Solving Problems of the Type $\log(x) = ax^2 + bx + c$

Confusion regarding Powers of Quotients Property and Change of Base Formula of Logs

Why $\log(x+1)=\log(1+\frac{1}{x})+\log(x)$?

How do you show that $\sum_{n=1}^{\infty}(-1)^{n}\dfrac{3n-1}{n^2 + n} = \log\left({32}\right) - 4$?

Natural Logarithm contradiction?

When is x +/- and when is it just positive when solving logarithms

Proving that $f(x) = \log(1 +x^2)$ is less than $|f'(x)|$ in a small neighbourhood around $0$

Basic Combinatorial Probability with Dice

Comparing expectations of logarithms of the random variables

Inequality with logarithm, missing one zero

Comparing logarithms with different bases

What is the one-to-one property and why does it work for logarithms?

A very strict inequality for $\ln n$ and $H_{n-1}$, with $n>2$, searching for proof

Trending Questions

Popular # Hahtags

Popular Questions