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

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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)} = $

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