Question

Me ajudem?
A integral de

Answer 1

$\boxed{ \int\limits { \sqrt{x} *(x+ \frac{1}{x})} \, dx }}$

$\boxed{u= \sqrt{x} }$

e tambem
$u= \sqrt{x} \\\\u^2=x$

e
$du = \frac{1}{2 \sqrt{x} } .dx\\\\du= \frac{1}{2u} .dx\\\\2u.du=dx$

substituindo na integral
$\int\limits {u(u^2+ \frac{1}{u} })*2u \, du \\\\\\2 \int\limits {u^2(u^2+ \frac{1}{u^2}) } \, du \\\\2 \int\limits{u^4+ \frac{u^2}{u^2} } \, dux \\\\\\\ \boxed{\boxed{2 \int\limits {u^4+1} \, du }}$

integrando
$(u^4+1).du= \frac{u^5}{5} +1u$

ficamos com 
$2 \int\limits {u^4+1} \, du \\\\\\ =2*( \frac{u^5}{5}+u) \\\\=2*( \frac{( \sqrt{x} )^5}{5}+ \sqrt{x} ) \\\\=\boxed{ \frac{2*x^{ \frac{5}{2} }}{5} + 2* x^{\frac{1}{2} }+ C}$

alternativa C