Evaluate the integral by making the given substitution.

Question

anonymous · Answer

$$\int\limits_{?}^{?}\sec(6x)\tan(6x) dx$$ u = 6x

anonymous · Answer

The more detailed the better, I'm trying to get better at trig

yttrium · Answer

well, it will yield to $$\int\limits \sec(u)\tan(u) \frac{ du }{ 6 }$$

campbell_st · Answer

well 

if y = sec(x)

then dy/dx = sec(x)tan(x) 

you don't need a substitution 

so 

sec(6x) = 6sec(6x)tan(6x) 

hope it helps

yttrium · Answer

then it is now easy to integrate. :))

anonymous · Answer

its asking me to use do the given substitution, going around the instructions doesn't get me points :p

yttrium · Answer

you can follow me, then :D

campbell_st · Answer

well use @Yttrium  version... it uses a substitution and makes sense...

campbell_st · Answer

but I'd be asking you're teacher why you would need a substitution for this question

yttrium · Answer

if you still have clarification, feel free to post it here :)

anonymous · Answer

thanks everyone >.<

yttrium · Answer

@campbell_st maybe theire topic is about integration by substitution and they're teacher just though of an example like this. :)

yttrium · Answer

***their

anonymous · Answer

no i get it, i was trying to convert sec to 1/cos and tan to sin/cos before trying to integrate it, it wasn't first nature to realize that the antiderivative is just sec(u)

yttrium · Answer

Alright then. Sudden realization! :D

anonymous · Answer

yeah! exactly haha thanks :)