New posts in trigonometric-integrals

How do I solve this integral $\displaystyle\int_{0}^{2\pi}e^{-\sin^{2}(x)}\cos\left(6x-\frac{\sin(2x)}{2}\right)\,dx$? [duplicate]

integration definite-integrals trigonometric-integrals

Closed form of $\int e^{i\csc^2(x)}dx=\int \cos\left(\csc^2(x)\right)dx+i\int \sin\left(\csc^2(x)\right)dx$

special-functions closed-form hypergeometric-function trigonometric-integrals fresnel-integrals

How to calculate $\int{\frac {x^2}{ ( x\cos x -\sin x ) ^2}}\,{\rm d}x$?

calculus indefinite-integrals trigonometric-integrals

Find $\int _0^1\frac{12\arctan ^2 x\ln (\frac{(1-x)^2}{1+x^2})-\ln ^3(\frac{(1-x)^2}{1+x^2})}{x}\:dx$

calculus integration definite-integrals logarithms trigonometric-integrals

what is the integral of $\int x\cos^2(\pi x)$

integration functions trigonometry definite-integrals trigonometric-integrals

Calculating $\int_0^\infty \frac{\sin(x)}{x} \frac{\sin(x / 3)}{x / 3} \frac{\sin(x / 5)}{x / 5} \cdots \frac{\sin(x / 15)}{x / 15} \ dx$

integration improper-integrals closed-form products trigonometric-integrals

Solve $\int_{0}^{\infty}\ln\Big(\frac{\sin^2(x)}{x^2}+1\Big)dx=?$

convergence-divergence improper-integrals trigonometric-integrals

Don't the derivatives of $\arctan x$ and $\operatorname{arccot} x$ imply they're negatives of each other?

integration trigonometric-integrals

Integration of $\int_0^{\pi/2}\frac{d\theta}{a^2+b^2\cos^2(\theta)}$ gives results such that $\tan(\pi/2)$ comes which is "undefined". How to proceed?

definite-integrals improper-integrals trigonometric-integrals

Is there an exact solution for $\large\int \frac{dx}{\tan^{-1}(x)}$?

integration summation recreational-mathematics inverse trigonometric-integrals

Evaluation the Elsasser function:$\text E(y,u)=\int_{-\frac12}^\frac12e^{\frac{2\pi uy\sinh(2\pi y )}{\cos(2\pi x)-\cosh(2\pi y)}}dx$ from MathWorld

sequences-and-series definite-integrals special-functions bessel-functions trigonometric-integrals

Evaluation of $\int\frac{\sqrt{\cos 2x}}{\sin x}\,dx$

calculus integration algebra-precalculus indefinite-integrals trigonometric-integrals

Trying to evaluate $\int \frac{1}{\sin(x)\cos^3(x)} \,dx$ and got stuck

integration indefinite-integrals trigonometric-integrals

How solve this nonlinear trigonometric differential equation

ordinary-differential-equations power-series special-functions trigonometric-integrals nonlinear-analysis

Series Representation of the Glasser function: $\text G(x)\mathop=\limits^\text{def} \int_0^x \sin(t\sin(t))dt\sim2\sqrt{\frac x\pi}$

sequences-and-series recreational-mathematics special-functions trigonometric-integrals chebyshev-polynomials

Fallacious proof involving trigonometry

calculus trigonometry proof-explanation fake-proofs trigonometric-integrals

Integral $\int_{-\infty}^{\infty} \arctan(e^x) \arctan(e^{-x})dx=\frac{7}{4}\zeta(3)$

integration definite-integrals improper-integrals riemann-zeta trigonometric-integrals

Prove that $ \int_{0}^{c} \frac{\sin(\frac{x}{2})x~dx}{\sqrt{\cos(x) - \cos(c)}} = \sqrt{2} \pi \ln(\sec(\frac{c}{2}))$

integration definite-integrals trigonometric-integrals

On $\int_0^{\pi} \operatorname{Si}^n(x) \ \mathrm{d}x $

calculus integration definite-integrals trigonometric-integrals

Evaluate $\int\frac{x^3}{\sqrt{81x^2-16}}dx$ using Trigonometric Substitution

calculus integration indefinite-integrals substitution trigonometric-integrals