integration: anti derivative of e^(2X+3)

[mindy88]

What's the anti derivative of e^(2X+3)?

i know that the formula for it is
e^(kx) is (1/K)e^(kx)

so...would it be
1/(2x+3) e^(2x+3)?

thanks

 

[pka]

Try: \(\displaystyle \L \left( {\frac{1}{2}} \right)e^{(2x + 3)} .\)
Do you see why?

 

[mindy88]

so, i would use only the 2 because that's the derivative of 2x+3?

 

[galactus]

Hello MIndy:

You can make a simple substitution and see it.

\(\displaystyle \L\\\int{e^{2x+3}}dx\)

Let \(\displaystyle \L\\u=2x+3, \;\ du=2dx, \;\ \frac{du}{2}=dx\)

\(\displaystyle \L\\\frac{1}{2}\int{e^{u}}du\)

 

[mindy88]

i didn't even think of using u-substitution

thanks for the help