`int t sec^2 2t dt` Evaluate the integral

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gsarora17 eNotes educator| Certified Educator


If f(x) and g(x) are differentiable functions, then


If we write f(x)=u and g'(x)=v, then


Now using the above method of integration by parts,




Now let's evaluate `inttan(2t)dt` by using the method of substitution,

Substitute `x=cos(2t),=>dx=-2sin(2t)dt`




substitute back `x=cos(2t)`



C is a constant



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