int frac{dx}{2sqrt{x}(1 + x)} = | vedclass

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

Question

(B) Let $I = \int \frac{dx}{2\sqrt{x}(1 + x)}$.Substitute $\sqrt{x} = t$. Then,differentiating both sides with respect to $x$,we get $\frac{1}{2\sqrt{

Vedclass · Accepted Answer

$	an^{-1}(\sqrt{x}) + c$

Vedclass · Answer

(B) Let $I = \int \frac{dx}{2\sqrt{x}(1 + x)}$.Substitute $\sqrt{x} = t$. Then,differentiating both sides with respect to $x$,we get $\frac{1}{2\sqrt{x}} dx = dt$.Substituting these into the integral,we get $I = \int \frac{dt}{1 + t^2}$.Using the standard integral formula $\int \frac{dt}{1 + t^2} = 	an^{-1}(t) + c$,we obtain $I = 	an^{-1}(t) + c$.Replacing $t$ with $\sqrt{x}$,the final result is $	an^{-1}(\sqrt{x}) + c$.

$\int \frac{dx}{2\sqrt{x}(1 + x)} = $

Similar Questions

Let $\int \frac{x^{1/2}}{\sqrt{1-x^3}} dx = \frac{2}{3} g(f(x)) + c$; then

$\int \frac{dx}{5 + 4\cos x} = $

Let $f(x) = \frac{x}{(1 + x^7)^{1/7}}$ and $g(x) = (f \circ f \circ f \circ f \circ f \circ f \circ f)(x)$. Then $\int x^5 g(x) dx$ equals (where $C$ is the constant of integration):

$\int \frac{\log \sqrt{x}}{3 x} d x$ is equal to

$\int \frac{\sin x}{\sqrt{5 \sin ^2 x+6 \cos ^2 x}} \,d x=$

Vedclass Test Series

Exam Paper Generator

Online Exam Module