Question

Doing another Integration:

Answer 1

\[\int 3^{x}e^{x}\]
I'm not sure where to start

Answer 2

this is what I was thinking first:
\[\int e^{xln{3}}e^{x}dx\]
then what u sub for xln3?

Answer 3

Have you learnt integration by parts ?

Answer 4

yes I have

Answer 5

this should do :
\(a^m\cdot a^n = a^{m+n}\)

Answer 6

That'd also do. Yes.

Answer 7

Otherwise it's a simple application of integrating by parts.

Answer 8

\[\int e^{xln3+x}dx\]

Answer 9

@shubhamsrg Integration by parts here is a bad idea

Answer 10

\[\frac{1}{ln(3)+1}\int e^{u}du\]

Answer 11

I = int(e^x 3^x)
= e^x 3^x - int(e^x 3^x ln 3)
I= e^x 3^x - I ln3
It's not too difficult to calculate I from here I guess.

Answer 12

answer=\[\frac{3^{x}e^{x}}{ln{3}+1}\]
right?

Answer 13

\[\int\limits 3^x e^x dx=3^x.e^x- \int\limits3^x \ln(3) e^xdx+C\]\[(1+\ln(3))\int\limits 3^x e^x dx=3^x.e^x+C\]\[\int\limits 3^x e^x dx=\frac{3^xe^x}{1+\ln(3)}+C'\]
Looks fine to me using by parts

Answer 14

that looks good ! below is, i think, a slightly better algebra..

\[\int 3^xe^x\,dx = \int (3e)^x\, dx = \int e^{x\ln (3e)}\, dx = \dfrac{e^{x\ln(3e)}}{\ln(3e)}+C = \dfrac{(3e)^x}{\ln(3e)}+C\]

Answer 15

Yes I could have simplified it more. I also forgot to add the constant.

Answer 16

\[\int b^x dx = \frac{b^x}{\ln b}\]

\[\int 3^xe^x dx = \int e^{(1+\ln 3)x}dx \]

\[b=e^{1+\ln 3}\]