Question

How do you integrate `\int \frac { ( x + 1) ^ { 2} } { \root[ 3] { x } } d x`?

Answer 1

`3/8*x^(8/3)+6/5*x^(5/3)+3/2*x^(2/3)+C`

Explanation:

`int (x+1)^2/x^(1/3)*dx`

=`int (x^2+2x+1)*x^(-1/3)*dx`

=`int x^(5/3)*dx`+`int 2x^(2/3)*dx`+`int x^(-1/3)*dx`

=`3/8*x^(8/3)+6/5*x^(5/3)+3/2*x^(2/3)+C`