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Question

Find the antiderivative of tan2(x)dx.


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Solution

Compute the antiderivative:

We can find the antiderivative as,

tan2(x)dx=sin2(x)cos2(x)dx

=1-cos2(x)cos2(x)dxsin2(x)+cos2(x)=1sin2(x)=1-cos2(x)

=1cos2(x)-cos2(x)cos2(x)dx

=sec2(x)-1dx1cos2(x)=sec2(x)

=sec2(x)dx-1dx

=tan(x)-x+Csec2(x)dx=tan(x),1dx=x

Hence, the antiderivative of tan2(x)dx is tan(x)-x+C, where C is constant of integration.


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