int frac{dx}{sin x+sqrt{3} cos x} equals,wher | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(C) To evaluate the integral $I = \int \frac{dx}{\sin x+\sqrt{3} \cos x}$,we multiply and divide by $2$: $I = \int \frac{dx}{2(\frac{1}{2} \sin x + \f

Vedclass · Accepted Answer

$\frac{1}{2} \ln \left|	an \left(\frac{x}{2}+\frac{\pi}{6}ight)ight|+c$

Vedclass · Answer

(C) To evaluate the integral $I = \int \frac{dx}{\sin x+\sqrt{3} \cos x}$,we multiply and divide by $2$: $I = \int \frac{dx}{2(\frac{1}{2} \sin x + \frac{\sqrt{3}}{2} \cos x)}$ Using the identity $\sin(x + \frac{\pi}{3}) = \sin x \cos \frac{\pi}{3} + \cos x \sin \frac{\pi}{3} = \frac{1}{2} \sin x + \frac{\sqrt{3}}{2} \cos x$,we get: $I = \frac{1}{2} \int \frac{dx}{\sin(x + \frac{\pi}{3})} = \frac{1}{2} \int \operatorname{cosec}(x + \frac{\pi}{3}) dx$ Using the standard formula $\int \operatorname{cosec} 	heta d	heta = \ln |	an(\frac{	heta}{2})| + c$: $I = \frac{1}{2} \ln |	an(\frac{x + \frac{\pi}{3}}{2})| + c = \frac{1}{2} \ln |	an(\frac{x}{2} + \frac{\pi}{6})| + c$.

$\int \frac{dx}{\sin x+\sqrt{3} \cos x}$ equals,where $c$ is an arbitrary constant.

Similar Questions

$\int \left\{ \frac{x}{a} + \frac{b}{x} + x^a + b^x + ab \right\} dx$ is equal to

Find the following integral: $\int \frac{d x}{x^{2}-6 x+13}$

$\int \frac{\sin 7x}{\sin 2x \sin 5x} dx =$

Find the following integral: $\int \left(x^{\frac{2}{3}} + 1\right) dx$

The value of $\int(1-\cos x) \operatorname{cosec}^2 x \, dx$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module