answer to the 2nd question:
f(x)= e^2x * (1+sin2x/1+cos2x)
=e^2x *((sinx+cosx)^2)/2.cos^2 x dx
=1/2 .e^2x *(tanx +1)^2 dx
=1/4 . e^t . (tan(t/2) +1)^2.dt {put 2x=t}
=1/4. e^2 . ( 1 + tan^t/2 +2tant/2) .dt
=1/4. e^t .( 2tant/2 + sec^2 (t/2)) dt
=1/4 . e^t .( f(t) + f'(t) ) .dt {put f(t)= 2tan(t/2)}
=1/4 .ef(t)
=1/4. e2tan(t/2)
=1/4. e2tanx {since t=2x}
keep posting such gud problems.............
rate me if i m correct
Moderation Team
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