## anonymous 5 years ago evaluate the integral of e^(3x)cos(4x)dx

1. anonymous

integration by parts where u=cos(4x) and dv=e^3x

2. anonymous

$\int\limits_{}^{}e ^{3x}(e ^{i4x}+e ^{-i4x})dx/2$$e ^{(3+4i)x}/(3+4i)+e ^{(3-4i)}/(3-4i)$

3. anonymous

or Euler's Identity which ever one comes easier to you..LOL

4. anonymous

the expression will be divided by 2.

5. anonymous

now you can just solve to get a ans.e^3x(3cos4x+4sin3c)/25+c where c is the integration constant.

6. anonymous

$\frac{1}{25} e^{3 x} (3 \text{Cos}[4 x]+4 \text{Sin}[4 x])$from Mathematica 8

7. anonymous

wow, u are so smart, you can copy answers out of a software package :/

8. anonymous

thank u :) u forgot the plus C robtobey

9. anonymous

10. anonymous

to do it algebraically involves two steps of integration by parts

11. anonymous

I think they most likely wanted it done algebraically

12. anonymous

first video does it algebraically ( which is most likely the way they want you to do it