int frac{sin 2x}{sin^2 x + 2cos^2 x} dx = | vedclass

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

Question

(D) Let $I = \int \frac{\sin 2x}{\sin^2 x + 2\cos^2 x} dx$. We know that $\sin^2 x + \cos^2 x = 1$,so the denominator becomes $\sin^2 x + \cos^2 x + \

Vedclass · Accepted Answer

$ -\log(1 + \cos^2 x) + C $

Vedclass · Answer

(D) Let $I = \int \frac{\sin 2x}{\sin^2 x + 2\cos^2 x} dx$. We know that $\sin^2 x + \cos^2 x = 1$,so the denominator becomes $\sin^2 x + \cos^2 x + \cos^2 x = 1 + \cos^2 x$. Thus,$I = \int \frac{\sin 2x}{1 + \cos^2 x} dx$. Let $t = 1 + \cos^2 x$. Then $dt = 2\cos x(-\sin x) dx = -\sin 2x dx$. So,$\sin 2x dx = -dt$. Substituting these into the integral,we get $I = \int \frac{-dt}{t} = -\log|t| + C$. Substituting back $t = 1 + \cos^2 x$,we get $I = -\log(1 + \cos^2 x) + C$.

$ \int \frac{\sin 2x}{\sin^2 x + 2\cos^2 x} dx = $

Similar Questions

In the following arrangement,$y = 1.0 \, mm$,$d = 0.24 \, mm$,and $D = 1.2 \, m$. The work function of the material of the emitter is $2.2 \, eV$. The stopping potential $V$ needed to stop the photocurrent will be....$V$

Which of the following can have a structure with $sp^3$ $C$ atoms only?

Beryllium is placed above magnesium in Group $2$. What happens when beryllium powder is added to a solution of $MgCl_2$?

Which part of the body secretes the hormone secretin?

Vedclass Test Series

Exam Paper Generator

Online Exam Module