what is the indefinite integral of tan(x)^4dx I believe I have the answer but I'm not sure

Question

lgbasallote · Answer

$\int (\tan x)^4 dx$ right? not $\int \tan (x^4)dx$

anonymous · Answer

yep tan(x) to the 4th

anonymous · Answer

Give me a second to type it up.

anonymous · Answer

i just want to know really if the answer is what I got 
((tan(x)^(3)/3)-(tan(x))+(x)+C)

lgbasallote · Answer

we can use trigonometric substitution $\int \tan^2 x (\tan^2 x)dx$ then let tan^2 x = sec^2 x - 1

$\int \tan^2x (\sec^2x - 1) dx$

now distribute...

$\int (\tan^2 x \sec^2 x)dx - \int \tan^2 xdx$


$\int (\tan^2 x \sec^2 x)dx - \int (\sec^2 x - 1)dx$


$\int (\tan^2 x \sec^2 x)dx - \int \sec^2 xdx - \int dx$

you an do it from tehre :p

anonymous · Answer

I got that ^^^^

anonymous · Answer

(1/3)tan^3(x)+x-tan(x)+C

lgbasallote · Answer

oh oh yeah should be + int dx

anonymous · Answer

Ok thanks my professor doesn't give the answers to exams if you get them wrong so I re did it and I guess I did it right so thanks guys