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SuperAbound's user avatar
SuperAbound
  • Member for 9 years, 10 months
  • Last seen more than 4 years ago
48 votes

Integration of the cardinal sine

36 votes
Accepted

Integral ${\large\int}_0^1\ln(1-x)\ln(1+x)\ln^2x\,dx$

30 votes

taylor series of $\ln(1+x)$?

26 votes
Accepted

Proof of $\int_0^\infty \frac{x^{\alpha}dx}{1+2x\cos\beta +x^{2}}=\frac{\pi\sin (\alpha\beta)}{\sin (\alpha\pi)\sin \beta }$

23 votes

How to find ${\large\int}_0^1\frac{\ln^3(1+x)\ln x}x\mathrm dx$

22 votes

Integral ${\large\int}_0^\infty\frac{\ln x}{1+x}\sqrt{\frac{x+\sqrt{1+x^2}}{1+x^2}}\ \mathrm dx$

21 votes

Closed-form of $\sum_{n=1}^\infty\frac{(-1)^{n+1}}{n}\Psi_3(n+1)=-\int_0^1\frac{\ln(1+x)\ln^3 x}{1-x}\,dx$

14 votes
Accepted

Integral $\int_1^{\sqrt{2}}\frac{1}{x}\ln\left(\frac{2-2x^2+x^4}{2x-2x^2+x^3}\right)dx$

13 votes
Accepted

Evaluating $\int_{0}^{\pi/3}\ln^2 \left ( \sin x \right )\,dx$

12 votes

Integrate $\left[\arctan\left(x\right)/x\right]^{2}$ between $-\infty$ and $+\infty$

10 votes
Accepted

Summation of infinite series, $\sum((3n+1)^{-1}-(3n+2)^{-1})$

10 votes
Accepted

Calculus Question: Improper integral $\int_{0}^{\infty}\frac{\cos(2x+1)}{\sqrt[3]{x}}\text dx$

8 votes

Integral $\int_0^{\pi/2} \theta^2 \log ^4(2\cos \theta) d\theta =\frac{33\pi^7}{4480}+\frac{3\pi}{2}\zeta^2(3)$

8 votes

How to find $\int_{0}^{\pi/2} \log ({1+\cos x}) dx$ using real-variable methods?

8 votes
Accepted

Prove that $\lim \limits_{x\to \infty}e^{\frac{\ln(x)}{x}}=1$

7 votes

How to show $n(n+1)(2n+1) \equiv 0 \pmod 6$?

7 votes

Evaluation of a dilogarithmic integral

7 votes

Integrals of integer powers of dilogarithm function

6 votes

Sum of the series $\frac{1}{2\cdot 4}+\frac{1\cdot3}{2\cdot4\cdot6}+\dots$

6 votes
Accepted

General form for $2\int_{0}^{\infty} \frac{1-t^2}{(1+t^2)((a+b)t^2+a-b)} \mathrm dt$

5 votes

Integral of Sinc Function Squared Over The Real Line

5 votes

Prove that $\int_0^1\frac{\ln(1-x)\ln^2x}{x-1}dx=\frac{\pi^4}{180}$

5 votes
Accepted

Trigonometric problem: $2^{\sin{x}} + 2^{\cos{x}} \ge 2^{(1-1/{\sqrt2})}$

5 votes
Accepted

Explain why $\big(\int_{-\infty}^{\infty}e^{-z^2/2}dz \big)^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(z^2 + u^2)/2}dzdu$

5 votes
Accepted

Antiderivative of $\frac{1}{1+\sin {x} +\cos {x}}$

5 votes

Integrals of integer powers of dilogarithm function

4 votes

How do you calculate the higher order deriviative of $x^n$?

4 votes

Evaluate $\int_0^\infty\frac{dl}{(r^2+l^2)^{\frac32}}$

4 votes

How do I find the perpendicular distance of a point from a plane?

4 votes

Evaluate $\int_0^{{\pi}/{2}} \log(1+\cos x)\, dx$