What is the integraton of Sin(2t)/1-cos(2t) dx ?

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Answer 1 · 2018-02-24T00:17:48

#ln|sin(t)|+C#

#intsin(2t)/(1-cos(2t))dt#

Recall the following identities:

#sin(2t)=2sin(t)cos(t)#

#cos(2t)=1-2sin^2(t)#

Rewrite the integral with the identities applied and simplify::

#int(2sin(t)cos(t))/(1-(1-2sin^2(t))dt#

#int(cancel2sin(t)cos(t))/(cancel2sin^2(t))dt#

#int(cancelsin(t)cos(t))/(cancelsin(t)sin(t))dt#

#int(cos(t)/sin(t))dt#

We can now use #u#-substitution:

#u=sin(t)#

#du=cos(t)dt#

#cos(t)dt # appears in the numerator of our integrand, so this substitution is valid:

#int(du)/u#

Integrate:

#int(du)/u=ln|u|+C#

Rewrite in terms of #t:#

#ln|sin(t)|+C#