$\smallint \,\,{e^{x\log a}}\,{e^x}\;dx$ is equal to

$\frac{{{a^x}}}{{\log \,\,ae}}\,\, + \,\,c$

$\frac{{{e^x}}}{{1 + \,\,{{\log }_e}\,\,a}}\,\, + \,\,c$

${\left( {ae} \right)^x} + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,{e^{x\log a}}\,{e^x}\;dx

is equal to

View answer and explanation

Correct option: D

\frac{{{{\left( {ae} \right)}^x}}}{{{{\log }_e}\,\,ae}}\,\, + \,\,c

Option D (

\frac{{{{\left( {ae} \right)}^x}}}{{{{\log }_e}\,ae}}\, + \,c

\) is correct because the integral of

e^{x\log a}e^x

simplifies to

\frac{{{{\left( {ae} \right)}^x}}}{{{{\log }_e}\,ae}}\, + \,c