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

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

$(a)\;\frac{1}{a} \bigg\{\frac{(ae^x+b)^{n+1}}{n+1}\bigg\}+c \qquad(b)\;\frac{1}{b} \bigg\{\frac{(ae^x+b)^{n+1}}{n+1}\bigg\}+c \qquad(c)\;\frac{1}{a} \bigg\{\frac{(ae^x+b)^{n}}{n}\bigg\}+c \qquad (d)\;\frac{1}{a} \bigg\{\frac{(be^x+a)^{n+1}}{n+1}\bigg\}+c$

1 Answer

$ae^x+b=t$
$ae^x.dx=dt$
$e^xdx=\large\frac{dt}{a}$
=> $\int \large\frac{1}{a} $$ \times t^n. dt$
=> $\large\frac{1}{a} \bigg( \large\frac{t^{n+1}}{n+1}\bigg)+c$
$\large\frac{1}{a} \bigg\{\frac{(ae^x+b)^{n+1}}{n+1}\bigg\}+c$
Hence a is the correct answer.
answered Dec 24, 2013 by meena.p
 
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