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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
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Integrate : $ \int x^2. e^{\Large x^3}. \cos (e^{\Large x^3}).dx$

$(a)\;\frac{1}{3} \sin (e^{x^3})+x^2+c \qquad(b)\;e^{x^3}+x^2+c \qquad(c)\;x^2+\sin (e^{x^3})+c\qquad (d)\;\frac{1}{3} \sin (e^{x^3})+c$
Can you answer this question?
 
 

1 Answer

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$e^{x^3}=t$
differentiate with x.
$3x^2. e^{x^3}dx=dt$
=>$x^2.e^{x^3}dx=\large\frac{dt}{3}$-----(i)
from equation (i)
=> $\int \cos t .\large\frac{dt}{3} $
=> $\large\frac{1}{3}$$ \sin t +c$
$\large\frac{1}{3} $$\sin (e^{x^3})$$+c$
Hence d is the correct answer.

 

answered Dec 23, 2013 by meena.p
 
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