Question

How do you find the antiderivative of `2x^(-2/3) dx`?

Answer 1

`6x^(1/3)+C`

Explanation:

We know that,
`color(red)(intx^ndx=x^(n+1)/(n+1)+C)`
`rArrint2x^-(2/3)dx=2(x^(-2/3+1)/(-2/3+1))+C=2(x^((-2+3)/3)/((-2+3)/3))+C=2(x^(1/3)/(1/3))+C=6x^(1/3)+C`