How do you integrate int cos^2(x) tan^3(x) dx?
1 Answer
Jul 23, 2016
I got:
cos^2x/2 - ln|cosx| + C
and Wolfram Alpha agrees.
Note that
color(blue)(int cos^2xtan^3xdx)
= int (sin^3x)/cosxdx
Then, you can use
= int ((1-cos^2x)sinx)/(cosx)dx
Hence:
= -int ((1-cos^2x)(-sinx))/(cosx)dx
= -int (1-u^2)/(u)du
= int (u^2 - 1)/(u)du
= int u - 1/udu
= u^2/2 - ln|u|
Re-substitute to get:
=> color(blue)(cos^2x/2 - ln|cosx| + C)