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

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

Question

(C) Let $I = \int \frac{dx}{\cos^2 x + \sin 2x}$.Divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec^2 x dx}{1 + 2 	an x}$.Let $t

Vedclass · Accepted Answer

$\frac{1}{2} \log |1 + 2 	an(x)| + C$

Vedclass · Answer

(C) Let $I = \int \frac{dx}{\cos^2 x + \sin 2x}$.Divide the numerator and denominator by $\cos^2 x$:$I = \int \frac{\sec^2 x dx}{1 + 2 	an x}$.Let $t = 1 + 2 	an x$. Then $dt = 2 \sec^2 x dx$,which implies $\sec^2 x dx = \frac{dt}{2}$.Substituting these into the integral:$I = \int \frac{1}{t} \cdot \frac{dt}{2} = \frac{1}{2} \int \frac{dt}{t} = \frac{1}{2} \log |t| + C$.Substituting back $t = 1 + 2 	an x$:$I = \frac{1}{2} \log |1 + 2 	an x| + C$.Thus,option $C$ is correct.

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

Similar Questions

$\int \frac{d x}{\sin \left(x-\frac{\pi}{3}\right) \cos x} = $

If $\int \sin^{-1}\left(\sqrt{\frac{x}{a+x}}\right) dx = A(x) + \text{constant}$, then $A(x) =$

$\int \sin^{\frac{-1}{2}}x \cos^{\frac{-7}{2}}x \, dx = $

If $n \geq 2$ is a natural number and $0 < \theta < \frac{\pi}{2}$,then $\int \frac{(\cos ^n \theta-\cos \theta)^{1 / n}}{\cos ^{n+1} \theta} \sin \theta d \theta =$

Evaluate the integral: $\int \frac{\ln(6x^2)}{x} \, dx$

Vedclass Test Series

Exam Paper Generator

Online Exam Module