# Questions tagged [trigonometric-integrals]

Relating to integrations consisting of only(mainly) trigonometric functions and/or requiring substitutions by/of trigonometric functions.

688 questions
Filter by
Sorted by
Tagged with
84 views

44 views

### On Integral consisting $\sin^2(f(x))$:

Consider the following integral: $$I(t)=\int_1^t\sin^2(f(x))dx$$ Here , $f(x)$ is monotonic for the given domain and is at least twice differentiable. Is there a result (in its full generality) ...
53 views

### Definite integral of exponentials and trig functions

Wikipedia has $$\int_{-\infty}^{\infty} e^{-ax^2} dx = \sqrt{\frac{\pi}{a}}$$ and $$\int_{-\infty}^{\infty} e^{-ax^2} e^{-2bx} dx= \sqrt{\frac{\pi}{a}} e^{\frac{b^2}{a}}$$ https://en....
132 views

### Integral $I(\tau_1,a,b) = \int_{\tau_1}^\infty d\tau_2\ \frac{1}{b^2 + \tau_2^2} \left(\pi - 2 \tan^{-1} \frac{\tau_2}{a} \right)^2$

I am looking at the integral: $$I(\tau_1,a,b) = \int_{\tau_1}^\infty d\tau_2\ \frac{1}{b^2 + \tau_2^2} \left(\pi - 2 \tan^{-1} \frac{\tau_2}{a} \right)^2, \tag{1}$$ where $\tau_1$ is real and $a, b$ ...
78 views

23 views

### Differential Equations Variations of Parameters and Constant Term

I have a general question about constant terms and trigonometric integrals. The question revolves about why pulling out this $\frac12$ term is important. This is the differential equation I was given\...
47 views

### Integral of trigonometric function with parameter

I need to solve the integral $$\int \frac{dx}{1+a\cos x}$$ for $a\>>0$ I tried to use the substitution $t=\tan\frac{x}{2}$ but unfortunately it doesn't seems to work here. after substitude all ...
58 views

44 views

### Where am I going wrong with the integral $\int\frac{1}{\sqrt{1-x^2}}dx$?

As my question says: Where am I going wrong with this integral? $$\int\frac{1}{\sqrt{1-x^2}}dx=\int(1-x^2)^{-1/2}dx=\int \frac{u^{-1/2}du}{-2x}=-\frac{1}{2x}2\sqrt{u}=-\frac{\sqrt{1-x^2}}{x}$$ For ...
### Solve indefinite integral $\int\frac{dx}{\sin^2{x}\cos^3{x}}$
I need to solve the integral below $$\int\frac{dx}{\sin^2{x}\cos^3{x}}$$ without using hyperbolic functions but using substitutions like $u=\tan{x}$, $u=\sin{x}$ or $u=\cos{x}$. Also, I know the ...