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

1 Answer
Feb 21, 2016

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