evaluate integration of cos2x/(cosx+sinx)^2
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Integral of cos2x / ((cosx + sinx) power 2)
It is quite difficult to write here. But I'm trying my best.
there is no integration or power sign so we represent these sign with some other sign.
# represent the integration, and
** represent the power sign
when you can do this in notebook please change these sign with integration and power.
we know that,
cos2x / (cos x + sin x)**2 = cos2x / (cos**2x + sin **2x + 2sinxcosx
= cos2x / (1 + sin2x)
Now, # cos2x / (cos x +sin x)**2 dx
= # cos2x / (1 + sin2x) dx
Let, 1+ sin2x = t
2cos2xdx = dt
# (cos2x / (cos x + sin x)**2) dx
= 1/2 # 1/t dt
= 1/2 log |t| + C
= 1/2 log | 1 + sin2x| + C
= 1/2 log |(sin x + cos x )**2| + C
= log | sin x + cos x | + C
I hope you can understand.
All the best!!
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