## appleduardo 2 years ago what is the integral of e^(senx) 4cosx dx ? how can i solve it?

1. appleduardo

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

2. geerky42

sen? You mean sec?

3. satellite73

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

4. appleduardo

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

5. appleduardo

i meant "sin":

6. tkhunny

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

7. appleduardo

thank you so much! but what happened with cos ?

8. tkhunny

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

9. appleduardo

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

10. tkhunny

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.

11. appleduardo

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

12. tkhunny

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