int frac{sin 2x}{sin^4 x + cos^4 x} , dx = | vedclass

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

Question

(B) Let $I = \int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx$. Divide the numerator and denominator by $\cos^4 x$: $I = \int \frac{2 \sin x \cos x}{\si

Vedclass · Accepted Answer

$	an^{-1}(	an^2 x) + c$

Vedclass · Answer

(B) Let $I = \int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx$. Divide the numerator and denominator by $\cos^4 x$: $I = \int \frac{2 \sin x \cos x}{\sin^4 x + \cos^4 x} \, dx = \int \frac{2 	an x \sec^2 x}{1 + 	an^4 x} \, dx$. Let $t = 	an^2 x$,then $dt = 2 	an x \sec^2 x \, dx$. Substituting these into the integral,we get: $I = \int \frac{dt}{1 + t^2} = 	an^{-1}(t) + c$. Replacing $t$ with $	an^2 x$,we obtain: $I = 	an^{-1}(	an^2 x) + c$.

$\int \frac{\sin 2x}{\sin^4 x + \cos^4 x} \, dx = $

Similar Questions

If $\int \frac{x^2}{\sqrt{1-x}} \,d x = p \sqrt{1-x} (3x^2 + 4x + 8) + c$ where $c$ is a constant of integration, then the value of $p$ is

$\int \frac{(1 + \log x)^2}{x} \, dx = $

$\int \frac{x^{n-1}}{x^{2n} + 4} dx =$

$\int x\sqrt{1 + x^2} \, dx = $

The value of $\int \frac{dx}{\sqrt{x}(x + 9)}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module