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

If $\int \frac{x^3 \, dx}{\sqrt{1+x^2}} = a(1+x^2) \sqrt{1+x^2} + b \sqrt{1+x^2} + c$ (where $c$ is a constant of integration),then the value of $3ab$ is

$\int \frac{x}{1 + x^4} \, dx = $

$\int \frac{\sin 2x}{4 \sin^2 x + 9 \cos^2 x} \, dx = $ (Where $C$ is a constant of integration).

$\int \sqrt{2 + \sin 3x} \cdot \cos 3x \, dx = $

$\int \frac{10 x^{9}+10^{x} \log _{e} 10}{x^{10}+10^{x}} d x$ equals

Vedclass Test Series

Exam Paper Generator

Online Exam Module