Question

найти интеграл
∫x³*√x^4+1 dx

Answer 1

$int x^3 sqrt{x^4+1} dx=frac{1}{4} int 4x^3 (x^4+1)^{frac{1}{2}}dx=$
$frac{1}{4} int (x^4+1)^{frac{1}{2}} d(x^4)=$
$frac{1}{4} int (x^4+1)^{frac{1}{2}} d(x^4+1)=$
$frac{1}{4} *frac{(x^4+1)^{frac{1}{2}+1}}{frac{1}{2}+1}$
$frac{1}{4}*frac{2}{3}*(x^4+1)^{frac{3}{2}}=$
$frac{(x^4+1)sqrt{x^4+1}}{6}$