anonymous
  • anonymous
integrate s4^s ds
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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dumbcow
  • dumbcow
\[\large \int\limits_{}^{}s*4^{s} ds\]
anonymous
  • anonymous
i think it is integration by parts u =s, dv= 4^s ds, du = ds, but what is v
dumbcow
  • dumbcow
4^s / ln(4) \[\int\limits_{}^{}a^{x} = \frac{a^{x}}{\ln(a)}\]

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dumbcow
  • dumbcow
yes you're right to use integration by parts
anonymous
  • anonymous
final answer is 4^s/ln4(s-1/ln4)+c
anonymous
  • anonymous
thanks, im doing web assign right now, and i keep getting stuck
dumbcow
  • dumbcow
hmm i get something a little different: \[\large \frac{s*4^{s}}{\ln(4)} -\frac{4^{s}}{(\ln(4))^{2}}\]
anonymous
  • anonymous
that is the same, mine is just simplified, i took out the s/ln4
anonymous
  • anonymous
how do you draw your equations so nice?
anonymous
  • anonymous
how to integrate e^(−θ) cos 4θ dθ
dumbcow
  • dumbcow
oh i see, i didn't read your answer right use the equation button, frac{}{} allows you to write nice fractions
dumbcow
  • dumbcow
to write exponents....x^{ }
anonymous
  • anonymous
\[e^{-\theta} cos4\theta d\theta\]
dumbcow
  • 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
dumbcow
  • dumbcow
The 2nd time should look like this: u = e^-x , dv = sin 4x du = -e^-x, v = -1/4 cos 4x
dumbcow
  • dumbcow
resulting in: \[\int\limits_{}^{}e^{-x}\cos(4x) = \frac{1}{4}e^{-x}\sin(4x)-\frac{1}{16}e^{-x}\cos(4x)-\frac{1}{16}\int\limits_{}^{}e^{-x}\cos(4x)\]
dumbcow
  • 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
dumbcow
  • dumbcow
do you follow?
anonymous
  • anonymous
? maybe, but the answer cannot contain an integral
dumbcow
  • 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
anonymous
  • anonymous
awesome, thanks!
dumbcow
  • 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
anonymous
  • anonymous
I appreciate your help, I hope you have a wonderful day

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