integrate 8

this is a good one. according to me it would be better if u remember the solution of this which i am going to post below.

given integral

=2(cos9x/2cosx/2)/1-2(2cos²3x/2-1) dx
now multiply and divide by cos3x/2

=2(cosx/2cos3x/2cos9x/2)/(3cos3x/2-4cos³3x/2)dx
=2(cosx/2cos3x/2cos9x/2)/-cos9x/2 dx

=-2cosx/2cos3x/2 dx

= -(cos2x+cosx)dx

therefore the answer is -sin2x/2 - sinx

Perfect . Only +c is remaining.

y remember ??

didi, this is one of the typical types i have seen among many that i have solved thats why...............

okie... nice trick ..

can be solevd even widout knowing the trick .. :)

tho a bit two or three more steps...