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Question

What is integral of cos2x?


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Solution

Step 1: Substitute u in the place 2x in the given integration

Let I=cos2xdx ….(1)

and 2x=u

Now differentiate the equation 2x=u with respect to x

2dx=du

dx=12du

Now putting dx=12du in equation (1)

I=12cosudu

Step 2: Apply the formula cosxdx=sinx+c

I=12cosudu

I=12sinu+c … where c is an integration constant

Putting u=2x

I=12sin2x+c

Hence the integral of cos2x is 12sin2x+c, where c is an integration constant.


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