Question

How do you find the indefinite integral of `int root3(7v)dv`?

Answer 1

The integral equals `3/28(7v)^(4/3) + C`

Explanation:

We let `u = 7v`. Then `du = 7dv` and `(dv)= (du)/7`.

`I = int root(3)(u) * (du)/7`

`I = 1/7int root(3)(u) du`

`I = 1/7int u^(1/3) du`

`I = 1/7(3/4u^(4/3)) + C`

`I = 3/28(7v)^(4/3) + C`

Hopefully this helps!