Question

What is `int x^2-sqrt(2x)dx`?

Answer 1

`1/3 x^3 - (2sqrt2)/3 x^(3/2) + c`

Explanation:

The standard integral is

`intax^n dx = (ax^(n+1))/(n+1) + c " where c is constant of integration"`

rewrite `sqrt(2x) = sqrt2 .x^(1/2)`

and apply the standard integral 'term by term'

`rArr int(x^2 - sqrt(2x))dx= x^3/3 - (sqrt2 x^(3/2))/(3/2) + c`

`= 1/3 x^3 - (2sqrt2)/3 x^(3/2) + c`