I have been doing couple of integration by parts and when I got to trig. integrals I get confuse, specially this problem.
Integral cos x^2 tan x^3 dx
I'm used to problems that has tan with sec^2's, cos with cos^2's etc
but not different trig functions such as cos and tan.
Let me practice on integration.
INT.[cos^2(X) tan^3(X)]dX
= INT.[cos^2(X) sin^3(X)/cos^3(x)]dX
= INT.[ sin^3(X) /cosX]dX
= INT.[{1 -cos^2(X)}sinX/cosX]dX
= INT.[sinX/cosX -sinXcosX]dX
= INT.[tanX -(1/2)sin(2X)]dX
= INT.[tanX]dX -(1/2)INT.[sin(2X)]dX
= ln[secX] -(1/2)(1/2)INT.[sin(2X)](2dX)
= ln[secX] -(1/4)[-cos(2X)]
= ln[secX] +(1/4)cos(2X) +C --------------answer.