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Int tan^6xdx

by reduction formula

((tanx)^5)/5 - int tan^4xdx

by reduction formula

((tanx)^5)/5 - ((tanx)^3)/3) + int tan^2xdx

tan^2x=sec^2x-1

((tanx)^5)/5 - ((tanx)^3)/3) + int sec^2xdx - int 1dx

((tanx)^5)/5 - ((tanx)^3)/3) + tanx - x + c

by reduction formula

((tanx)^5)/5 - int tan^4xdx

by reduction formula

((tanx)^5)/5 - ((tanx)^3)/3) + int tan^2xdx

tan^2x=sec^2x-1

((tanx)^5)/5 - ((tanx)^3)/3) + int sec^2xdx - int 1dx

((tanx)^5)/5 - ((tanx)^3)/3) + tanx - x + c