## anonymous 5 years ago How do you integrate e^2x sin(3x)dx?

1. bahrom7893

Use integration by parts. Btw when is this due?

2. anonymous

its a revision, we cant figure it out

3. bahrom7893

No i just meant i have to do my own hw too, so do u need this like right away or by tonite or by 2morro mornin?

4. bahrom7893

ill just do it now

5. anonymous

we would just like to know what to do with the sin(3x)

6. anonymous

thanks!

7. bahrom7893

ima write this out on paper and email it to u. what's ur email?

8. anonymous

moca341@hotmail.com .. thank you :)

9. bahrom7893

np

10. bahrom7893

almost done...

11. anonymous

great!

12. bahrom7893

i will take separate pix and email them one by one, the whole solution won't fit lol

13. anonymous

thats fine! haha

14. bahrom7893

okay emailed it

15. bahrom7893

ask me if u have any questions, either here or by email and Fan if I helped!

16. bahrom7893

did u get it?

17. anonymous

It helped a lot, but i dont really get it!, ill try to figure it out! thanks a lot!

18. bahrom7893

no, ask me which part don't you understand?

19. bahrom7893

I think it might the place where I let that one integral be capital i

20. anonymous

i dont even understand the first line, dont worry about it!

21. bahrom7893

Oh okay so first I used integration by parts. See the stuff in the circle: I said Let u = e^(2x), then what is du/dx? du/dx = derivative of u = 2e^(2x), multiply both sides by dx to get: du = 2e^(2x)dx

22. anonymous

i dont see where the 1/3 cos (3x) comes from

23. bahrom7893

Oh okay that's just the integral of Sin(3x)

24. bahrom7893

I will work it out here: After that I said let dv/dx = Sin(3x), well then what's V? v is the integral of dv/dx with respect to x. V = Integral(dv/dx, dx) $v = \int\limits_{}^{}Sin(3x)dx$

25. bahrom7893

Here you have to use a simple substitution: Let a = 3x; then da = 3 dx. Now you have 3x in your integral, but you still need a 3 in front of dx. To do so, multiply and divide by 3, same as multiplying by 1

26. anonymous

ok, i get it, thanks a lot!

27. bahrom7893

$v = \int\limits_{}^{}Sin(3x)*(3/3)*dx = (1/3) *\int\limits_{}^{}Sin(3x)*3*dx$

28. bahrom7893

Now you have both a and da; your integral simplifies to: $(1/3)\int\limits_{}^{}Sin(a)*da$

29. bahrom7893

that's it then integrate as u would a regular sin and in the end replace a by 3x