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what is the integral of e^(senx) 4cosx dx ? how can i solve it?
 one year ago
 one year ago
what is the integral of e^(senx) 4cosx dx ? how can i solve it?
 one year ago
 one year ago

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appleduardoBest ResponseYou've already chosen the best response.0
\[\int\limits_{}^{}e ^{sen x} 4\cos x dx\]
 one year ago

satellite73Best ResponseYou've already chosen the best response.0
try \(u=\sin(x), du=\cos(x)dx\) and you get it in one step
 one year ago

appleduardoBest ResponseYou've already chosen the best response.0
i got \[[e^{sen x} +c] [4 sen x + c]\] is that correct?
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
\(\int e^{\sin(x)}\cdot 4\cos(x)\;dx\) Following satellite73 suggestion u = sin(x) du = cos(x)dx This gives \(\int e^{u}\cdot 4\;du = 4\cdot e^{u} + C\) Substitute back to where we started. \(4\cdot e^{\sin(x)} + C\) Be careful, consistent, and confident.
 one year ago

appleduardoBest ResponseYou've already chosen the best response.0
thank you so much! but what happened with cos ?
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
It's all in there with the nature of the substitution. See the definition of du.
 one year ago

appleduardoBest ResponseYou've already chosen the best response.0
so in this case cos represents the derivative for sin in the formula , right?
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
That is where it came from. You can't just substitute a function. The nature of dx changes when you do that. Is English your first language? The answer to this question might help other folks understand where "sen(x)" came from.
 one year ago

appleduardoBest ResponseYou've already chosen the best response.0
haha yeah, uhmm but right now im studying in a spanishspeaking country, so sometimes (unconsciously) isay or write spanish :/ . thank you so!
 one year ago

tkhunnyBest ResponseYou've already chosen the best response.1
No worries  as long as you don't mind freaking people out when you accidentally write the spanish versions of things. Good work!
 one year ago
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