Question

the Anti derivatives of (√x + 1/√x) equals to

Answer 1

HELLO DEAR,

the anti derivatives of (√x + 1/√x) is a function of x whose derivative is (√x + 1/√x).​

now,
$\bold{\int{(\sqrt{x} + 1/\sqrt{x})}\,dx}$

$\bold{\Rightarrow \int{\sqrt{x}}\,dx + \int{1/\sqrt{x}}\,dx}$

$\bold{\Rightarrow \int{x^{1/2}}\,dx + \int{x^{-1/2}}\,dx}$

$\bold{\Rightarrow \frac{x^{3/2}}{3/2} + \frac{x^{1/2}}{1/2}}$

$\bold{\Rightarrow \frac{2x^{3/2}}{3} + 2x^{1/2} + C}$

where, C is the arbitrary constant
Hence, anti derivatives of (√x + 1/√x) is (2x^{3/2}/3 + 2x^{1/2}) + C.

I HOPE ITS HELP YOU DEAR,
THANKS