## anonymous 4 years ago integrate s4^s ds

1. dumbcow

$\large \int\limits_{}^{}s*4^{s} ds$

2. anonymous

i think it is integration by parts u =s, dv= 4^s ds, du = ds, but what is v

3. dumbcow

4^s / ln(4) $\int\limits_{}^{}a^{x} = \frac{a^{x}}{\ln(a)}$

4. dumbcow

yes you're right to use integration by parts

5. anonymous

6. anonymous

thanks, im doing web assign right now, and i keep getting stuck

7. dumbcow

hmm i get something a little different: $\large \frac{s*4^{s}}{\ln(4)} -\frac{4^{s}}{(\ln(4))^{2}}$

8. anonymous

that is the same, mine is just simplified, i took out the s/ln4

9. anonymous

how do you draw your equations so nice?

10. anonymous

how to integrate e^(−θ) cos 4θ dθ

11. dumbcow

oh i see, i didn't read your answer right use the equation button, frac{}{} allows you to write nice fractions

12. dumbcow

to write exponents....x^{ }

13. anonymous

$e^{-\theta} cos4\theta d\theta$

14. dumbcow

integration by parts again...here you will have to do it twice u = e^-x , dv = cos 4x du = -e^-x, v = 1/4 sin4x

15. dumbcow

The 2nd time should look like this: u = e^-x , dv = sin 4x du = -e^-x, v = -1/4 cos 4x

16. dumbcow

resulting in: $\int\limits_{}^{}e^{-x}\cos(4x) = \frac{1}{4}e^{-x}\sin(4x)-\frac{1}{16}e^{-x}\cos(4x)-\frac{1}{16}\int\limits_{}^{}e^{-x}\cos(4x)$

17. dumbcow

then notice the integrals are exactly the same, so think combining like terms add 1/16 integral to other side then all you have to do is divide by a constant

18. dumbcow

do you follow?

19. anonymous

? maybe, but the answer cannot contain an integral

20. dumbcow

thats right, so imagine you treat the integrals like variables and combine like terms move it over to other side where the original integral is

21. anonymous

awesome, thanks!

22. dumbcow

your welcome here is a great resource for checking your work http://www.wolframalpha.com/input/?i=integrate+e%5E-x+*+cos%284x%29+dx

23. anonymous

I appreciate your help, I hope you have a wonderful day