Question

Oblicz całki:
x\/x-x^4\/x ....
(Zadanie w załączniku)

Answer 1

[tex]\int\frac{x\sqrt x-x\sqrt[4]x}{\sqrt[3]x}\, dx =\int\frac{x*x^{\frac{1}{2}}-x*x^{\frac{1}{4}}}{x^{\frac{1}{3}}}\, dx =\int\frac{x^{\frac{3}{2}}-x^{\frac{5}{4}}}{x^{\frac{1}{3}}}\, dx =\int\left(\frac{x^{\frac{3}{2}}}{x^{\frac{1}{3}}}-\frac{x^{\frac{5}{4}}}{x^{\frac{1}{3}}}\right)\, dx =[/tex]

[tex]=\int\left(x^{\frac{3}{2}-\frac{1}{3}}-x^{\frac{5}{4}-\frac{1}{3}}\right) \, dx =\int\left(x^{\frac{9}{6}-\frac{2}{6}}-x^{\frac{15}{12}-\frac{4}{12}}\right) \, dx =\int\left(x^{\frac{7}{6}}-x^{\frac{11}{12}}\right) \, dx =[/tex]

[tex]=\frac{6}{13}x^{\frac{13}{6}}-\frac{12}{23}x^{\frac{23}{12}}+C[/tex]