exponential integration

G

Guest

Guest
integrate
(5^x)(e^x) dx

I cannot figure out this one...please help
 
How about rewriting: \(\displaystyle \L\mbox{ 5^x = \left(e^{\ln{(5)}}\right)^x = e^{\left(x\ln{(5)}\right)}}\)
 
In general \(\displaystyle \L
\int {a^x dx = \frac{{a^x }}{{\ln (a)}}\mbox{ if }\ a > 0}\)

Also recall that \(\displaystyle \L
\left( {5^x } \right)\left( {e^x } \right) = \left( {5e} \right)^x\)

So let \(\displaystyle \L
a = 5e.\)
 
Then the integrand can be written \(\displaystyle \mbox{ e^{\left(x(\ln{(5)} + 1)\right)}}\).

And I'm sure you can integrate \(\displaystyle \mbox{e^{ax}}\).
 
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