Find an anti-derivative (or integral) of the following functions by the method of inspection.

sin 2x

Method: To find the anti derivative of a function by inspection 
Steps: 1. In this method we look for a function whose derivative is the given function. For Example: if we need to find anti derivative of x², we know that derivative of x³ is 3x². Therefore, the variable terms comes out to be the same.
2. After that balance out the coefficients of variables by dividing and multiplying suitable terms. From above example if [we divide x³ by 3 we will get the answer as x². Hence, we can say that anti derivative of x² is x³/3.

Now, similarly,

We know that

Therefore, the anti-derivative of sin2x is