Can substitution be used to solve these trigonometric integrals?

[Steel_City82]

the two problems are
the integral of (sec^3x)(tan x)dx
and the integral of (sec^4x)(tan x)dx

will substitution work for both of these problems

 

[Tide]

Why don't you just try substitution and see if it works?

 

[Steel_City82]

I did and I got an answer for both, but for some reason I think I should follow the rule and change the sec^4x to (tan+1)(sec^2x)

and you don't get the same answer when you do it like that

if you just strait substitute you get sec^7x/5
and if you change a sec^2x to 1+tan you get tan^4x/2
I think, that's if I am even doing it right

 

[TD]

Replace tan(x) by sin(x)/cos(x) (bearing in mind that sec(x) = 1/cos(x)) and the substitution should be clear