If int frac{d x}{sqrt{sin ^3 x cos x}}=g(x)+c | vedclass

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

Question

(B) Given,$\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$.We can rewrite the integral as:$\int \frac{d x}{\sqrt{\sin ^4 x \cdot \frac{\cos x}{\sin x

Vedclass · Accepted Answer

$\frac{-2}{\sqrt{	an x}}$

Vedclass · Answer

(B) Given,$\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$.We can rewrite the integral as:$\int \frac{d x}{\sqrt{\sin ^4 x \cdot \frac{\cos x}{\sin x}}} = \int \frac{d x}{\sin ^2 x \sqrt{\cot x}}$This simplifies to:$\int \operatorname{cosec}^2 x \cdot (\cot x)^{-1/2} d x$Let $t = \cot x$,then $dt = -\operatorname{cosec}^2 x d x$,which implies $\operatorname{cosec}^2 x d x = -dt$.Substituting these into the integral:$\int -t^{-1/2} dt = -\frac{t^{1/2}}{1/2} + c = -2\sqrt{t} + c$Substituting back $t = \cot x$:$-2\sqrt{\cot x} + c = -\frac{2}{\sqrt{	an x}} + c$Therefore,$g(x) = -\frac{2}{\sqrt{	an x}}$.

If $\int \frac{d x}{\sqrt{\sin ^3 x \cos x}}=g(x)+c$,then $g(x)$ is equal to

Similar Questions

The integral $\int \frac{1}{\sqrt[4]{(x-1)^{3}(x+2)^{5}}} dx$ is equal to : (where $C$ is a constant of integration)

$\int \frac{dx}{(a^2 + x^2)^{3/2}}$ is equal to

$\int \frac{\sqrt{\cot x}}{\sin 2x} dx =$

$\int (x^{21} + x^6 + x^3)(2x^{18} + 7x^3 + 14)^{1/3} dx = $

$\int \sin ^3(x) \cdot \cos ^3(x) \, dx =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module