how can i integrate sin x/((cos x)^5)

Question

anonymous · Answer

Is this the function?
$$f(x)=\frac{ \sin(x) }{ \cos^{5}(x) }$$

anonymous · Answer

sin(x)/cos(x)=tan(x)
1/cos(x)^4=sec(x)^4
u=sec(x)
derivative of sec(x)=sec(x) * tan(x)
du=sec(x) * tan(x)
int(u^3*du)
(u^4)/4
(sec(x)^4)/4

anonymous · Answer

yes

anonymous · Answer

Cool, I wrote it out but got beaten to the punch. But that answer is correct, make sense?

anonymous · Answer

Also, you could have made u=cos(x) to save you a step.

anonymous · Answer

ok john, is notme's step correct?

anonymous · Answer

It is correct, but most people don't know the derivative of sec(x) off-hand so I found it easier to work this way. Both will yield the same solution, but it does show the importance of knowing your trig derivatives/integrals and how they come to be. Here's my solution for reference.

anonymous · Answer

thank you bro

anonymous · Answer

Glad to help