How do you integrate #(tanx)^5*(secx)^4dx#?
1 Answer
Nov 26, 2016
Explanation:
Writing this as:
#inttan^5xsec^4xdx#
Rewriting to leave all
#=inttan^5xsec^2xsec^2xdx#
#=inttan^5x(tan^2x+1)sec^2xdx#
Letting
#=intu^5(u^2+1)du#
#=intu^7du+intu^5du#
#=u^8/8+u^6/6+C#
#=tan^8x/8+tan^6x/6+C#