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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $\int \sqrt x .e^{\sqrt x} dx $

$(a)\;2 \sqrt x -e^{\sqrt x }-4 \sqrt x e^{\sqrt x}+c \\(b)\;(2x -4 \sqrt x +4)e^{\sqrt x}+c \\(c)\;(1-4 \sqrt x).e^{\sqrt x }+c \\ (d)\;None$
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1 Answer

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$\sqrt x =t $
$\large\frac{1}{2}$$ \sqrt x dx=dt$
=> $2 \int t^2.e^t.dt$
=> $ 2 [e^t.\large\frac{t^2}{3}$$ -2 \int t.e^t dt]+c$
=> $ 2 [t^2 .e^t -2 (t.e^t)+2e^t]+c$
=> $ 2 [x.e^{\sqrt x} -2 (\sqrt x .e^{\sqrt x})+2e^{\sqrt x}]+c$
$(2x -4 \sqrt x +4)e^{\sqrt x}+c$
Hence b is the correct answer.
answered Jan 2, 2014 by meena.p
 
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