int frac{dtheta}{sin theta cos^3 theta} = | vedclass

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

Question

(C) Let $I = \int \frac{d	heta}{\sin 	heta \cos^3 	heta}$.Divide the numerator and denominator by $\cos^4 	heta$:$I = \int \frac{\sec^4 	heta \,

Vedclass · Accepted Answer

$\log 	an 	heta + \frac{1}{2} 	an^2 	heta + c$

Vedclass · Answer

(C) Let $I = \int \frac{d	heta}{\sin 	heta \cos^3 	heta}$.Divide the numerator and denominator by $\cos^4 	heta$:$I = \int \frac{\sec^4 	heta \, d	heta}{	an 	heta} = \int \frac{\sec^2 	heta (1 + 	an^2 	heta) \, d	heta}{	an 	heta}$.Substitute $t = 	an 	heta$,so $dt = \sec^2 	heta \, d	heta$:$I = \int \frac{1 + t^2}{t} \, dt = \int \left( \frac{1}{t} + t ight) \, dt$.Integrating with respect to $t$:$I = \log |t| + \frac{t^2}{2} + c$.Substituting back $t = 	an 	heta$:$I = \log |	an 	heta| + \frac{	an^2 	heta}{2} + c$.

$\int \frac{d\theta}{\sin \theta \cos^3 \theta} = $

Similar Questions

$\int \frac{e^x \, dx}{\sqrt{1 - e^{2x}}} = $

If $\int_1^3 x^n \sqrt{x^2-1} dx = 6$,then $n = $

$ \int \frac{1}{\sqrt{x}+x \sqrt{x}} d x $

$\int \frac{2 t+1}{t^2+t+1} d t=$

Let $f(x) = \int \frac{x^2 dx}{(1 + x^2)(1 + \sqrt{1 + x^2})}$ and $f(0) = 0$,then the value of $f(1)$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module