Question

How do you find the following indefinite integral of `(x^(2)+sin(2x))dx`?

Answer 1

I found: `x^3/3+sin^2(x)+c`

Explanation:

Consider:
`int(x^2+sin(2x))dx=`
`intx^2dx+intsin(2x)dx=`
`=x^3/3+int2sin(x)cos(x)dx=` but `d[sin(x)]=cos(x)dx`;
`x^3/3+2intsin(x)d[sin(x)]=x^3/3+cancel(2)sin^2(x)/cancel(2)+c`