Question

Найти первообразные для функции (2x+1)*корень x

Answer 1

$y=(2x+1)sqrt{x}=2xsqrt{x}+sqrt{x}=2x^{3/2}+x^{1/2}\\F(x)=int (2x^{3/2}+x^{1/2})dx=2cdot frac{x^{5/2}}{5/2} + frac{x^{3/2}}{3/2}+C=\\= frac{4sqrt{x^5}}{5}+frac{2sqrt{x^3}}{3}+C$