int {frac{{{e^{sqrt x }}}}{{sqrt x }}dx} = | vedclass

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Question

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

Vedclass · Accepted Answer

$2e^{\sqrt{x}}$

Vedclass · Answer

(C) Let $I = \int \frac{e^{\sqrt{x}}}{\sqrt{x}} dx$.Substitute $\sqrt{x} = t$.Then,differentiating both sides with respect to $x$,we get $\frac{1}{2\sqrt{x}} dx = dt$,which implies $\frac{1}{\sqrt{x}} dx = 2 dt$.Substituting these into the integral:$I = \int e^t (2 dt) = 2 \int e^t dt$.Integrating $e^t$ gives $e^t$,so:$I = 2 e^t + C$.Substituting back $t = \sqrt{x}$:$I = 2 e^{\sqrt{x}} + C$.

$\int {\frac{{{e^{\sqrt x }}}}{{\sqrt x }}dx} = $

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