Question

с математикой с интеграломи

Answer 1

$\int\limits \frac{3x + 2 {x}^{2} }{ \sqrt[4]{x} } dx = \int\limits( \frac{3x}{ \sqrt[4]{x} } + \frac{2 {x}^{2} }{ \sqrt[4]{x} } )dx = \\ = \int\limits(3 {x}^{1 - \frac{1}{4} } + 2 {x}^{2 - \frac{1}{4} } )dx = \int\limits3 {x}^{ \frac{3}{4} } dx +\int\limits2 {x}^{ \frac{7}{4} } dx = \\ = 3 \times \frac{ {x}^{ \frac{7}{4} } }{ \frac{7}{4} } + 2 \times \frac{ {x}^{ \frac{11}{4} } }{ \frac{11}{4} } + C= \\ = \frac{12}{7} x \sqrt[4]{ {x}^{3} } + \frac{8}{11} {x}^{2} \sqrt[4]{ {x}^{3} } + C$