Evaluate the following. intsin^2xcdottan xdx

Tobias Ali

Tobias Ali

Answered question

2021-02-24

Evaluate the following.
sin2xtanxdx

Answer & Explanation

Khribechy

Khribechy

Skilled2021-02-25Added 100 answers

The given integral is:
sin2xtanxdx
we have to evaluate the given integral.
Let the given integral be I.
Therefore,
I=sin2xtanxdx
=(1cos2x)tanxdx
(because sin2x+cos2x=1 therefore sin2x=1cos2x)
=(1cos2x)sinxcosxdx (because tanx=sinxcosx)
Now let cosx=t
therefore,
d(cosx)=dt
sinxdx=dt
sinxdx=dt
now substitute these values in the integral I.
Therefore,
I=(1t2)dtt
=(t21t)dt
=(t2t1t)dt
=(t1t)dt
=tdtdtt
=t22ln|t|+C
where C is the constant of integration
now substitute the value of t that is t=cosx in the integral I.
therefore,
I=t22ln|t|+C
=(cosx)22ln|cosx|+C
cos2x2ln|cosx|+C
therefore,
I=sin2xtanxdx=cos2x2ln|cos<

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