sorry buddy as I m not going to explain it fully.
write tan(x) and cot(x) in sinx and cosx.
after doing this ur question would have cos^2(x)-sin^2(x) in numerator and sqrt(cos(x)sin(x)) * (1+6sin(x)cos(x) )in denominator.
just put sinxcosx =t^2
ur question will become 2dt/(1+3t^2)
which u can do easily.
Let f(x) =
Now write sin2x in terms of sinx + cos x
that is, sin 2x = ( sinx + cosx )2 - 1
So, f(x) =
Now, your integral,
for this, substitute sinx + cosx = t,
u get numerator as dt
I becomes =
substitute t2 - 1 = z2,
this is the tan-1 form
i think u can do it now...
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