Question

integration of x^3+ 3x^2+ 2 upon root x dx​

Answer 1

Step-by-step explanation:

$\int \frac{ {x}^{3} + 3 {x}^{2} + 2 }{ \sqrt{x} } dx$

$= \int ({x}^{ \frac{5}{2} } + 3 {x}^{ \frac{3}{2} } + 2 {x}^{ - \frac{1}{2} } )dx$

$= \int {x}^{ \frac{5}{2} } dx + \int3 {x}^{ \frac{3}{2} } dx + \int2 {x}^{ - \frac{1}{2} } dx$

$= \frac{2}{7} {x}^{ \frac{7}{2} } + 3 \times \frac{2}{5} {x}^{ \frac{5}{2} } +2 \times 2 {x}^{ \frac{1}{2} } + c$

$= \frac{2}{7} {x}^{ \frac{7}{2} } + \frac{6}{5} {x}^{ \frac{5}{2} } + 4 \sqrt{x} + c$