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Home  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Integral Calculus

Integrate : $\int \sqrt x e^{\large (x)^{3/2}} \cos (e^{\large(x)^{3/2}}. dx$

\[\begin {array} {1 1} (a)\;\sin (e^{x^{1/2}})+c \\ (b)\;\frac{2}{3} \sin (e^{x^{3/2}})+c \\ (c)\;\sin (e^{x^{3/2}})+c \\ (d)\;None \end {array}\]

1 Answer

$e^{(x)^{\large 3/2}}=t$
$e^{(x)^{\large 3/2}}.$$\large\frac{3}{2} . (x) ^{1/2} $$dx=dt$
=> $\sqrt {x} .e^{(x)^{\large 3/2}}.dx=\large\frac{2}{3}$$dt$
=> $\int\large\frac{2}{3} $$\cos (t) .dt$
$\large\frac{2}{3}$$ \sin (e^{x^{3/2}})+c$
Hence b is the correct answer.
answered Dec 19, 2013 by meena.p
 
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