integral

[Mikieman]

How could I take the integral of (e^3lnx + e^3x)dx =

If I was to use u substitution what would I let U equal.

 

[Unco]

If that is

\(\displaystyle \L \mbox{ \int{ e^{(3\ln{x})} + e^{(3x)} dx}\)

You can just simplify: \(\displaystyle \mbox{ e^{(3\ln{x})} = e^{(\ln{(x^3)})} = x^3}\)

and then integrate.

 

[mattflint50]

i did it out and i got x^4/4 + e^3x +c. Is that correct?

 

[mattflint50]

wait, no Mikieman that can't be the answer. Let someone explain it to you.

 

[Mikieman]

I got x^4/4 + 3e^3x +c as the anser. Is this correct

 

[galactus]

\(\displaystyle \int{e^{3x}}dx\)

Let \(\displaystyle u=3x, du=3dx, \frac{1}{3}du=dx\).

So we have:

\(\displaystyle \frac{1}{3}\int{e^{u}}du=\frac{1}{3}e^{3x}\)