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justaguide eNotes educator| Certified Educator

We have to find the integral of cos 2x.

Int[ cos 2x dx]

let 2x = u

du = 2*dx

dx = (1/2)*du

=> Int [ cos u * (1/2) du]

=> (1/2) sin u + C

substitute u = 2x

=> (1/2) sin 2x + C

The required integral of cos 2x is (1/2)*sin 2x + C

nvoron23 | Student

integral is antiderivative of the function.

in this case, a derivative would use the chain rule, wherareas the antiderivative or the integral would use the same, except in the opposite direction.  Thus, Integral of of cos 2x is (1/2)*sin 2x

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