integral

Mikieman

New member
Joined
Jan 22, 2006
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4
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.
 
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.
 
e3xdx\displaystyle \int{e^{3x}}dx

Let u=3x,du=3dx,13du=dx\displaystyle u=3x, du=3dx, \frac{1}{3}du=dx.

So we have:

13eudu=13e3x\displaystyle \frac{1}{3}\int{e^{u}}du=\frac{1}{3}e^{3x}
 
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