Oblicz calke nieoznaczona[latex] int { frac{ (x^{2}-1) ^{3} }{x} } , dx [/latex]

zauważ, że: [latex]frac{(x^2-1)^3}{x}=frac{x^6-3x^4+3x^2-1}{x}=x^5-3x^3+3x-frac{1}{x} \ hbox{Jest to prosta calka. Liczyc bede ze wzoru:} \ int x^a dx= frac{x^{a+1}}{a+1} \ \ int frac{(x^2-1)^3}{x}dx=int (x^5-3x^3+3x-frac{1}{x})dx= \ = int x^5 dx-3int x^3dx+3int xdx -int frac{dx}{x}= \ = frac{x^{5+1}}{5+1}-3 cdot frac{x^{3+1}}{3+1}+3 cdot frac{x^{1+1}}{1+1}-ln x +C = \ oxed{=frac{x^6}{6}-frac{3x^4}{4}+frac{3x^2}{2}-ln x+C}[/latex]