Newbetuts

Let $f:[a,b]\to\mathbb R$ be Riemann integrable and $f>0$. Prove that $\int_a^bf>0$. (No Measure theory) [closed]

How to prove the second mean value theorem for definite integrals

How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac14,\frac14;\frac34;-\alpha\right)=\beta\,$?

How to show that $ \int^{\infty}_{0} \frac{\ln (1+x)}{x(x^2+1)} \ dx = \frac{5{\pi}^2}{48} $ without complex analysis?

Integral $\int_{-\infty}^{\infty}\frac{\cos(s \arctan(ax))}{(1+x^2)(1+a^2x^2)^{s/2}}dx$

Integral $\int_0^{\pi/4}\frac{dx}{{\sin 2x}\,(\tan^ax+\cot^ax)}=\frac{\pi}{8a}$

Integral $\int_0^1 \frac{dx}{\sqrt[3]{x(1-x)}(1-x(1-x))}$

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

How can I solve $\int_0^1\frac{\arctan(x^2)}{1+x^2}\,\mathrm dx$?

When change of variable makes an empty interval

How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

Evaluating $\int_0^{\pi/2}\operatorname{arcsinh}(2\tan x)\,dx$

evaluate this definited integral using the differentiating under the integral sign Leibniz rule.q

Seeking Methods to solve $ I = \int_{0}^{\frac{\pi}{2}} \frac{\arctan\left(\sin(x)\right)}{\sin(x)}\:dx$

Evaluating $\int_0^{\pi/4} \ln(\tan x)\ln(\cos x-\sin x)dx=\frac{G\ln 2}{2}$

Integration with $\ln(x)$ in the denominator

New posts in definite-integrals

Definite integral of even powers of Cosine.

What is known about sums of the form $\sum_{n=-\infty}^{\infty} \operatorname{sinc} (n^{p})$?

Evaluating $\int_0^1\frac{3x^4+ 4x^3 + 3x^2}{(4x^3 + 3x^2 + 2x+ 1)^2}\, dx$

Let $f:[a,b]\to\mathbb R$ be Riemann integrable and $f>0$. Prove that $\int_a^bf>0$. (No Measure theory) [closed]

How to prove the second mean value theorem for definite integrals

How to show an infinite number of algebraic numbers $\alpha$ and $\beta$ for $_2F_1\left(\frac14,\frac14;\frac34;-\alpha\right)=\beta\,$?

How to show that $ \int^{\infty}_{0} \frac{\ln (1+x)}{x(x^2+1)} \ dx = \frac{5{\pi}^2}{48} $ without complex analysis?

Integral $\int_{-\infty}^{\infty}\frac{\cos(s \arctan(ax))}{(1+x^2)(1+a^2x^2)^{s/2}}dx$

Integral $\int_0^{\pi/4}\frac{dx}{{\sin 2x}\,(\tan^ax+\cot^ax)}=\frac{\pi}{8a}$

Integral $\int_0^1 \frac{dx}{\sqrt[3]{x(1-x)}(1-x(1-x))}$

Prove that $\int_0^\infty \frac{\ln x}{x^n-1}\,dx = \Bigl(\frac{\pi}{n\sin(\frac{\pi}{n})}\Bigr)^2$

Closed-form of $\int_0^1 \operatorname{Li}_p(x) \, dx$

How can I solve $\int_0^1\frac{\arctan(x^2)}{1+x^2}\,\mathrm dx$?

When change of variable makes an empty interval

How to prove $\int_{0}^{\infty} \frac{(1-x^2) \, \text{sech}^2\left(\frac{\pi x}{2} \right)}{(1+x^2)^2}\, dx = \frac{\zeta(3)}{\pi}$?

Evaluating $\int_0^{\pi/2}\operatorname{arcsinh}(2\tan x)\,dx$

evaluate this definited integral using the differentiating under the integral sign Leibniz rule.q

Seeking Methods to solve $ I = \int_{0}^{\frac{\pi}{2}} \frac{\arctan\left(\sin(x)\right)}{\sin(x)}\:dx$

Evaluating $\int_0^{\pi/4} \ln(\tan x)\ln(\cos x-\sin x)dx=\frac{G\ln 2}{2}$

Integration with $\ln(x)$ in the denominator