Question

integration of (√x)+(1/√x) is​

Answer 1

Answer:

$→\int( \sqrt{x} + \frac{1}{ \sqrt{x} } )dx \\ = \int \sqrt{x} dx + \int \frac{1}{ \sqrt{x} } dx \\ = \int {x}^{ \frac{1}{2} } dx + \int {x}^{ - \frac{1}{2} } dx \\ = \frac{ {x }^{ (\frac{1}{2} + 1 )} }{( \frac{1}{2} + 1) } + \frac{ {x}^{( - \frac{1}{2} + 1) } }{( - \frac{1}{2} + 1) } + C \\ = \frac{ {x}^{ \frac{3}{2} } }{ \frac{3}{2} } + \frac{ {x}^{ \frac{1}{2} } }{ \frac{1}{2} } + C \\ = \boxed{ \frac{2}{3} {x}^{ \frac{3}{2} } + 2 {x}^{ \frac{1}{2} } +C}✓$