Question

Qual a integral [x(2x-1)+√x]dx

Answer 1

$\int\limits {x(2x-1+ \sqrt{x} )} \, dx \\ \\ \int\limits {(2x^2-x+ \sqrt{x} )} \, dx \\ \\ 2\int\limits {x^2} \, dx- \int\limits {x} \, dx+ \int\limits {x^{ \frac{1}{2} }} \, dx \\ \\ 2. \frac{x^3}{3}- \frac{x^2}{2} + \frac{x^{ \frac{3}{2} }}{ \frac{3}{2} } \\ \\ \frac{2x^3}{3}- \frac{x^2}{2} + \frac{2x^{ \frac{3}{2} }}{3} \\ \\ \boxed{ \frac{4x^3-3x^2+4 \sqrt{x^3} }{6} +C}$