Question

A integral de f(x)=sqrt(x)(x+1/x) é:

Answer 1

$\int \sqrt{x}\;(x+ \frac{1}{x} ) dx\\\\ \int (x*\sqrt{x}+ \frac{\sqrt{x}}{x} ) dx\\\\ \int (x*x^{ \frac{1}{2}} + \frac{x^{ \frac{1}{2} }}{x} )dx\\\\ \int (x^{1+ \frac{1}{2} }+x^{ \frac{1}{2}-1 })dx\\\\ \int (x^{ \frac{3}{2} }+ x^\frac{-1}{2})dx = \frac{x^{ \frac{5}{2} }}{ \frac{5}{2} } + \frac{x^{ \frac{1}{2} } }{\frac{1}{2}} +C= \boxed{\boxed{\frac{2x^{ \frac{5}{2} }}{5}+ 2x^{ \frac{1}{2} }+C}}$