The value of int frac{dx}{sqrt{x}(x + 9)} is | vedclass

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

Question

(D) Let $I = \int \frac{dx}{\sqrt{x}(x + 9)}$.Substitute $\sqrt{x} = t$. Then $x = t^2$,which implies $dx = 2t \, dt$.Substituting these into the inte

Vedclass · Accepted Answer

$\frac{2}{3}	an^{-1}\left(\frac{\sqrt{x}}{3}ight)$

Vedclass · Answer

(D) Let $I = \int \frac{dx}{\sqrt{x}(x + 9)}$.Substitute $\sqrt{x} = t$. Then $x = t^2$,which implies $dx = 2t \, dt$.Substituting these into the integral,we get:$I = \int \frac{2t \, dt}{t(t^2 + 9)} = 2 \int \frac{dt}{t^2 + 3^2}$.Using the standard integral formula $\int \frac{du}{u^2 + a^2} = \frac{1}{a} 	an^{-1}\left(\frac{u}{a}ight) + C$,we have:$I = 2 \cdot \frac{1}{3} 	an^{-1}\left(\frac{t}{3}ight) + C = \frac{2}{3} 	an^{-1}\left(\frac{\sqrt{x}}{3}ight) + C$.

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

Similar Questions

$\int \frac{(\sin^{-1} x)^{\frac{3}{2}}}{\sqrt{1-x^2}} dx =$

$\int \frac{\csc^2 x}{1 + \cot x} dx = $

The integral $\int \frac{(x^8-x^2) dx}{(x^{12}+3x^6+1) \tan^{-1}(x^3+\frac{1}{x^3})}$ is equal to:

The value of $\int \frac{x^{2} d x}{\sqrt{x^{6}+a^{6}}}$ is equal to

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

Vedclass Test Series

Exam Paper Generator

Online Exam Module