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

Question

appleduardo · Answer

$$\int\limits_{}^{}e ^{sen x} 4\cos x  dx$$

geerky42 · Answer

sen? You mean sec?

anonymous · Answer

try $u=\sin(x), du=\cos(x)dx$ and you get it in one step

appleduardo · Answer

i got  $$[e^{sen x} +c] [4 sen x + c]$$ is that correct?

appleduardo · Answer

i meant "sin":

tkhunny · Answer

$\int e^{\sin(x)}\cdot 4\cos(x)\;dx$

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.

appleduardo · Answer

thank you so much! but what happened with cos ?

tkhunny · Answer

It's all in there with the nature of the substitution.  See the definition of du.

appleduardo · Answer

so in this case cos represents the derivative for sin in the formula , right?

tkhunny · Answer

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.

appleduardo · Answer

haha yeah, uhmm but right now im studying in a spanish-speaking country, so sometimes (unconsciously) isay or write spanish :/ . thank you so!

tkhunny · Answer

No worries - as long as you don't mind freaking people out when you accidentally write the spanish versions of things.  Good work!