User Kamal Saleh - Mathematics Stack Exchange

15 votes

How should I evaluate this indefinite integral involving natural logarithm?

answered Nov 4, 2023 at 0:07

6 votes

How to multiply two different logarithms.

answered Dec 13, 2022 at 22:25

6 votes

Accepted

Using L'hospitals rule when right hand limit and left hand limit are different

answered Dec 12, 2023 at 14:19

5 votes

Accepted

Integral of a function under a square root

answered Jan 5, 2023 at 18:54

5 votes

Calculate $\sum_{n=2}^{\infty}\left (n^2 \ln (1-\frac{1}{n^2})+1\right)$

answered Oct 31, 2022 at 15:23

5 votes

Accepted

A closed form expression of $\sum_{n \ge 0} \biggl( \sum_{k=1}^n \frac{1}{k} \biggr)z^n$

answered Dec 8, 2022 at 21:21

5 votes

Accepted

Solving $\sin x=\cos 2x$ by expressing left side as $\cos (\pi/2-x)$ doesn't give correct solution

answered Jan 26, 2023 at 22:03

4 votes

Book recommendation for "intermediate level"problem book on calculus.

answered Jul 24, 2023 at 6:34

4 votes

What other tricks and techniques can I use in integration?

answered Feb 15, 2023 at 19:11

4 votes

What other tricks and techniques can I use in integration?

answered Mar 2, 2023 at 0:38

4 votes

How to prove $\lim_{x \to \infty}\frac{\log x}{\sqrt{x}} = 0$?

answered Dec 28, 2022 at 2:37

4 votes

Accepted

Show $\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right] = \zeta(s)$

answered Dec 25, 2023 at 16:08

4 votes

Accepted

Compute $\int_{0}^{e}\frac{\ln(1-W(x))}{x}dx$

answered Dec 12, 2023 at 14:25

4 votes

An accurate, rapidly converging estimate of $\sum_{j = 1}^{\infty}\frac 1 {j^2}$ (the Basel Problem) using only elementary calculus

answered Jan 23 at 18:16

3 votes

Accepted

Integrating $\int_{0}^{\infty} \frac{\tanh \left(\frac{x}{2}\right)+\tanh (2 x)}{x}\left(e^{\frac{3 x}{2}}-1\right)^{2} e^{-4 x} \mathrm{~d}x$

answered Feb 11 at 2:36

3 votes

Evaluation of a limit at infinity

answered Jan 5 at 4:14

3 votes

Prove $\lim_{n\to\infty}\left(\frac{n^3}{\sqrt{n^2+a}}-\frac{n^3}{\sqrt{n^2+b}}\right)=\frac{b-a}2.$

answered Dec 6, 2022 at 16:38

3 votes

Challenging: The inverse function of $y=\left(\frac{1}{8}\right)^{1-x}$

answered Sep 29, 2022 at 18:08

3 votes

Using u-subsitution to integrate $ \int_{0}^{1} e^{3 x^{3}-2 x}\left(9 x^{2}-2\right) d x $

answered Sep 2, 2022 at 15:29

3 votes

Find the limit of $\sqrt[9]{5x^2 + 1} / \sqrt[7]{4x^3 - 1}$ as $x \to \infty$

answered Sep 28, 2023 at 18:18

3 votes

How do we prove that $\int_{-\infty}^\infty\frac{x^2+1}{x^6+x^2+1}\mathrm{d}x$ converges according to the comparison test?

answered Mar 9, 2023 at 5:11

3 votes

Accepted

finding sum of infinity power series

answered May 22, 2023 at 15:35

3 votes

Power series of $\frac{1}{7+x}$

answered Nov 8, 2023 at 5:13

3 votes

How to derive the formula for $n$-th Fibonacci numbers ($F_n = \frac{a^n-b^n}{a-b}$)?

answered Oct 22, 2023 at 5:12

3 votes

Grade 12 Functions

answered Nov 12, 2023 at 21:49

3 votes

Accepted

Relation between $\phi$ and $\pi$

answered Feb 9, 2023 at 18:54

3 votes

Accepted

How do we evaluate this integral containing log

answered Mar 29, 2023 at 19:13

2 votes

Accepted

How to solve the given differential equation $xg(f(x))f'(g(x))g'(x)= f(g(x))g'(f(x))f'(x)$?

answered Mar 30, 2023 at 16:54

2 votes

What is the name of this differential equation: $\frac{\partial f(x, y)}{\partial x} + \frac{\partial g(x, y)}{\partial y} = 0$?

answered Feb 28, 2023 at 1:26

2 votes

How to prove $\sqrt{\frac{x+1}{x^3-x^2}}=\frac{\frac1x+1}{\sqrt{x^2-1}}$

answered Mar 7, 2023 at 16:37

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191 Answers

How should I evaluate this indefinite integral involving natural logarithm?

How to multiply two different logarithms.

Using L'hospitals rule when right hand limit and left hand limit are different

Integral of a function under a square root

Calculate $\sum_{n=2}^{\infty}\left (n^2 \ln (1-\frac{1}{n^2})+1\right)$

A closed form expression of $\sum_{n \ge 0} \biggl( \sum_{k=1}^n \frac{1}{k} \biggr)z^n$

Solving $\sin x=\cos 2x$ by expressing left side as $\cos (\pi/2-x)$ doesn't give correct solution

Book recommendation for "intermediate level"problem book on calculus.

What other tricks and techniques can I use in integration?

What other tricks and techniques can I use in integration?

How to prove $\lim_{x \to \infty}\frac{\log x}{\sqrt{x}} = 0$?

Show $\frac{1}{s-1}+\sum_{n=1}^{\infty}\left[\frac{1}{n^s}+\frac{1}{s-1}\left(\frac{1}{(n+1)^{s-1}} - \frac{1}{n^{s-1}}\right)\right] = \zeta(s)$

Compute $\int_{0}^{e}\frac{\ln(1-W(x))}{x}dx$

An accurate, rapidly converging estimate of $\sum_{j = 1}^{\infty}\frac 1 {j^2}$ (the Basel Problem) using only elementary calculus

Integrating $\int_{0}^{\infty} \frac{\tanh \left(\frac{x}{2}\right)+\tanh (2 x)}{x}\left(e^{\frac{3 x}{2}}-1\right)^{2} e^{-4 x} \mathrm{~d}x$

Evaluation of a limit at infinity

Prove $\lim_{n\to\infty}\left(\frac{n^3}{\sqrt{n^2+a}}-\frac{n^3}{\sqrt{n^2+b}}\right)=\frac{b-a}2.$

Challenging: The inverse function of $y=\left(\frac{1}{8}\right)^{1-x}$

Using u-subsitution to integrate $ \int_{0}^{1} e^{3 x^{3}-2 x}\left(9 x^{2}-2\right) d x $

Find the limit of $\sqrt[9]{5x^2 + 1} / \sqrt[7]{4x^3 - 1}$ as $x \to \infty$

How do we prove that $\int_{-\infty}^\infty\frac{x^2+1}{x^6+x^2+1}\mathrm{d}x$ converges according to the comparison test?

finding sum of infinity power series

Power series of $\frac{1}{7+x}$

How to derive the formula for $n$-th Fibonacci numbers ($F_n = \frac{a^n-b^n}{a-b}$)?

Grade 12 Functions

Relation between $\phi$ and $\pi$

How do we evaluate this integral containing log

How to solve the given differential equation $xg(f(x))f'(g(x))g'(x)= f(g(x))g'(f(x))f'(x)$?

What is the name of this differential equation: $\frac{\partial f(x, y)}{\partial x} + \frac{\partial g(x, y)}{\partial y} = 0$?

How to prove $\sqrt{\frac{x+1}{x^3-x^2}}=\frac{\frac1x+1}{\sqrt{x^2-1}}$