Question

como resolver esta integral  2x³ √x dx

Answer 1

$\int2x^3\sqrt{x}\,dx=\\\\\int2\sqrt{x^6\cdot\,x}\,dx=\\\\\int2\sqrt{x^7}\,dx=\\\\\int2x^\frac{7}{2}\,dx=\\\\2\int\,x^\frac{7}{2}\,dx=\\\\2\left[\frac{2}{9}\cdot\,x^{\frac{7}{2}+1}\right]=$

$2\left[\frac{2}{9}\cdot\,x^{\frac{9}{2}}\right]=\\\\\frac{4\cdot\,x^{\frac{9}{2}}}{9}+c=\\\\\frac{4\sqrt[2]{x^9}}{9}+c=\\\\\boxed{\frac{4x^4\sqrt{x}}{9}+c}$