Basic anti-derivitive question:

[Obnoxious]

Can someone please show me the exact steps to finding the F(x) of:

y = {sec x tan x dx

[revprez]

Can someone please show me the exact steps to finding the F(x) of:

y = {sec x tan x dx

 

Do you know the trig identities?

[Ducky Havok]

Okay, there aren't many steps to show for this one. You just have to realize that the derivative of Sec(x) is Sec(x)Tan(x), so your answer is just Sec(x)+C

[Callipygous]

if you sexy(sec) you have a sexy tan (sec tan)

 

if you have a tan your sexy squared. (tan --> sec sec)

 

 

: )

[Obnoxious]

J33bu5, so it's almost memorization!! I must've been thinking too hard...

[Pat Says]

You can also easily show it using the trig identities like revprez pointed out. It works out fairly simple (you said you wanted to do it by hand so I assumed you meant with steps involved)

 

Ssin[x]/(cos[x])^2 dx u=cos[x] du=-sin[x]

 

-S (1/u^2) du

=-(-1/u) + c

=1/cos[x]+c= sec[x] + c

 

Simple as that