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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Integral Calculus
0 votes

Integrate : $ \int e^x (a e^x+b)^n. dx$

\[\begin {array} {1 1} (a)\;\frac{1}{a} \bigg[\frac{(ae^x+b)^n+1}{n+1}\bigg] \\ (b)\;\bigg[\frac{(ae^x+b)^n+1}{n+1}\bigg] \\ (c)\;\bigg[\frac{(ae^x+b)+1}{a(n+1)}\bigg] \\ (d)\;None \end {array}\]
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1 Answer

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$=> ae^{x}+b=t$
$ ae^{x}.dx=dt$
$=> \int \large\frac{1}{a}$$ (t^n).dt$
$=> \large\frac{1}{a}$$ \bigg(\large\frac{t^{n+1}}{n+1} \bigg)$$+c$
$\large\frac{1}{a} \bigg[\frac{(ae^x+b)^n+1}{n+1}\bigg]$
Hence a is the correct answer.
answered Dec 19, 2013 by meena.p
 
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