New posts in trigonometric-integrals

Area bounded by $\cos x+\cos y=1$

definite-integrals area geometric-probability trigonometric-integrals

Help to evaluate $\int_{0}^{\pi}\sec(x)\sqrt{\tan\left(\frac{x}{2}\right)}\ln^n\tan\left(\frac{x}{2}\right)dx$

calculus integration definite-integrals trigonometric-integrals

Prove $\sum_{n=1}^\infty \text{Ci}(\pi n)=\frac{\ln(2)-\gamma}{2}$

sequences-and-series summation trigonometric-integrals

Trying to evaluate $\int_{0}^{\infty}\frac{\ln(1+x^3)}{1+x^3}\frac{dx}{1+x^3}$

calculus integration definite-integrals trigonometric-integrals

Exact expression of a trigonometric integral

integration analysis closed-form trigonometric-integrals

Improper integral of sin(x)/x from zero to infinity [duplicate]

integration improper-integrals trigonometric-integrals

Explain why $\int_0^\infty\frac{\sin{4x}}{x}\prod\limits_{k=1}^n \cos\left(\frac{x}{k}\right) dx\approx\frac{\pi}{2}$

calculus integration sequences-and-series pi trigonometric-integrals

Integral Help - $\int \frac {\sqrt{u^2-a^2}}{u}du$

calculus integration trigonometric-integrals

Solving $\int_0^{\frac{\pi}{2}}\frac{1}{\sin^{2n}(x) + \cos^{2n}(x)}\:dx$

integration definite-integrals gamma-function trigonometric-integrals beta-function

Solving $\int_0^{\infty} \ln^m(x)\sin\left(x^n\right)\:dx$

integration definite-integrals trigonometric-integrals

Calculate $\int_0^{2\pi} \tan \frac{\theta}8 d\theta $ using complex analysis

complex-analysis definite-integrals line-integrals trigonometric-integrals

An interesting integral $\cos(x)\cos(x^2)\cos(x^3)...$

trigonometric-integrals upper-lower-bounds

Prove $\int_0^1 \frac{4\cos^{-1}x}{\sqrt{2x-x^2}}\,dx=\frac{8}{9\sqrt{\pi}}\left(9\Gamma(3/4)^2{}_4F_3(\cdots)+\Gamma(5/4)^2{}_4F_3(\cdots)\right)$

definite-integrals closed-form gamma-function hypergeometric-function trigonometric-integrals

How can I continue my proof that the difference of cosine integrals is the Euler Mascheroni constant?

calculus power-series trigonometric-integrals euler-mascheroni-constant

Evaluate $\int_{0}^{\pi/2}{\frac{d\theta}{{\left(\cos^3{\theta}+\sin^3{\theta}\right)}^{2/3}}}$

integration definite-integrals trigonometric-integrals

About integrating $\sin^2 x$ by parts

calculus integration indefinite-integrals trigonometric-integrals

Evaluate $\int_0^\pi \frac{\sin\frac{21x}{2}}{\sin \frac x2} dx$ (from MIT Integration Bee)

integration definite-integrals contest-math trigonometric-integrals

Showing $\int_0^{\int_0^u{\rm sech}vdv}\sec vdv\equiv u$ and $\int_0^{\int_0^u\sec vdv}{\rm sech} vdv\equiv u$

hyperbolic-functions trigonometric-integrals

Close-form for integral $T(n)=\int_0^{\pi/2}\frac{1}{1+\sin^n(x)}dx$

real-analysis integration definite-integrals closed-form trigonometric-integrals

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

sequences-and-series reference-request definite-integrals trigonometric-integrals trigonometric-series