New posts in trigonometric-integrals

Closed form for the integral $\int_0^{\pi/2} \frac{x-\sin x}{\tan x-x} dx$

definite-integrals closed-form trigonometric-integrals

How is $\frac{\sin^2x}{\cos^2x+1}=\frac{\tan^2x}{1+\sec^2x}$?

trigonometry indefinite-integrals trigonometric-integrals

An Intriguing Identity: $\cos(2x) \overset{?}{=} \log_{\cos(1)}\frac{\cos(\cos(x))}{\cos(\sin(x))}$

trigonometry proof-verification logarithms trigonometric-integrals

Alternative and more direct proof that an integral is independent of a parameter

integration definite-integrals contour-integration alternative-proof trigonometric-integrals

Question about finite analog of $\int_0^\infty \frac{\sin x\sinh x}{\cos (2 x)+\cosh \left(2x \right)}\frac{dx}{x}=\frac{\pi}{8}$

integration definite-integrals contour-integration closed-form trigonometric-integrals

A closed form for $\int_0^\pi \lvert \sin(m t) \cos(n t) \rvert \, \mathrm{d} t$

calculus integration limits definite-integrals trigonometric-integrals

Compute close-form of $\int_0^{\frac\pi2}\frac{dt}{\sin t+\cos t+\tan t+\cot t+\csc t+\sec t}$

calculus integration definite-integrals closed-form trigonometric-integrals

Residue Theorem and Complex analysis (cauchy residue theorem) [duplicate]

residue-calculus trigonometric-integrals

Find $\int_0^{2\pi}\frac1{5-4\cos x}\ dx$

calculus integration definite-integrals trigonometric-integrals

Evaluating $\left.\int_0^{\pi/2}\sqrt{1+\frac1{\sqrt{1+\tan^nx}}}\text dx \middle/\int_0^{\pi/2}\sqrt{1-\frac1{\sqrt{1+\tan^nx}}}\text dx\right.$

calculus integration definite-integrals ratio trigonometric-integrals

Question on integral containing exponential and sine function

real-analysis integration indefinite-integrals trigonometric-integrals

Integrate $\int_{0}^{\pi}{\frac{x\cos{x}}{1+\sin^{2}{x}}dx}$

integration definite-integrals trigonometric-integrals calculus

Show that $\int_0^\pi f(\sin x)\,\mathrm{d}x = 2\int_0^{\pi/2}f(\sin x) \, \mathrm{d}x$ [closed]

integration trigonometry definite-integrals trigonometric-integrals

Calculate $\int\left( \sqrt{\tan x}+\sqrt{\cot x}\right)dx$ [duplicate]

integration indefinite-integrals trigonometric-integrals

Integration of secant [duplicate]

calculus integration indefinite-integrals trigonometric-integrals

Use $\int_0^{\pi/2}\frac{1}{1 + \cos x + \sin x}dx = \ln 2$ to find $\int_0^{\pi/2}\frac{x}{1 + \cos x + \sin x}dx$

calculus integration derivatives definite-integrals trigonometric-integrals

$\int_0^{\frac{\pi}{2}} \frac{cos(x)}{p\sin(x) + q\cos(x)}dx$, where $p,q$ are positive constants

calculus definite-integrals trigonometric-integrals

How to evaluate the integral $\int \sqrt{1+\sin(x)} dx$

calculus integration trigonometry trigonometric-integrals