Question

Найти неопр.интеграл
1) и 2)

Answer 1

$intlimits {frac{sqrt{x}- sqrt[3]{x^2} -x^{-frac{1}{2}}}{xsqrt{x}}} , dx = intlimits {frac{x^{frac{1}{2}}- x^{frac{2}{3}} -x^{-frac{1}{2}}}{x^{frac{3}{2}}}} , dx =\\ = intlimits {[x^{frac{1}{2}-frac{3}{2}}- x^{frac{2}{3}-frac{3}{2}} -x^{-frac{1}{2}-frac{3}{2}}]} , dx =\\ = intlimits {[x^{-1}- x^{-frac{5}{6}} -x^{-2}}]} , dx =\\ = intlimits {frac{1}{x}} , dx - intlimits {x^{-frac{5}{6}}} , dx - intlimits {x^{-2}} , dx =\\ =ln|x|-6x^{frac{1}{6}}+x^{-1}+C$

$intlimits {frac{x^5+3x^3}{x^2}} , dx = intlimits {[x^3+3x]} , dx =\\ =frac{x^4}{4}+frac{3x^2}{2}+C$