The correct option is B 2/3(1+e^x)^3/2+c let e^x=t e^xdx= dt #160;∫√(1+t) dt= 23 (1+t)^32 +c = 23(1+e^x)^3/2+c ...

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Property 7

∫ ex√1+exdx=

Question

$\int e^{x} \sqrt{1 + e^{x}} d x =$

(1 + e^{x})^{\frac{3}{2}} + c

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\frac{2}{3} (1 - e^{x})^{3 / 2} + c

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(1 - e^{x})^{3 / 2} + c

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\frac{2}{3} (1 + e^{x})^{3 / 2} + c

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Solution

The correct option is B $\frac{2}{3} (1 + e^{x})^{3 / 2} + c$
let $e^{x} = t$
$e^{x} d x = d t$
$\int \sqrt{1 + t} d t = \frac{2}{3} (1 + t)^{\frac{3}{2}} + c$
$=$ $\frac{2}{3} (1 + e^{x})^{3 / 2} + c$

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