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

1. appleduardo Group Title

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

2. geerky42 Group Title

sen? You mean sec?

3. satellite73 Group Title

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

4. appleduardo Group Title

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

5. appleduardo Group Title

i meant "sin":

6. tkhunny Group Title

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

thank you so much! but what happened with cos ?

8. tkhunny Group Title

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

9. appleduardo Group Title

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

10. tkhunny Group Title

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 Group Title

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 Group Title

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