Tìm: a) tích phân 1/ x^4 dx;                   b) tích phân x căn x dx (x lớn hơn 0); 

a) \(\int {\frac{1}{{{x^4}}}} dx = \int {{x^{ - 4}}} dx = \frac{{{x^{ - 3}}}}{{ - 3}} + C = \frac{{ - 1}}{{3{x^3}}} + C\).

b) \(\int {x\sqrt x } dx = \int {{x^{\frac{3}{2}}}} dx = \frac{{{x^{\frac{3}{2} + 1}}}}{{\frac{3}{2} + 1}} + C = \frac{2}{5}{x^{\frac{5}{2}}} + C = \frac{2}{5}{x^2}\sqrt x + C\).

c) \(\int {\left( {\frac{3}{x} - 5\sqrt[3]{x}} \right)} dx = 3\int {\frac{1}{x}} dx - 5\int {{x^{\frac{1}{3}}}} dx\)

\( = 3\ln \left| x \right| - 5.\frac{{{x^{\frac{1}{3} + 1}}}}{{\frac{1}{3} + 1}} + C = 3\ln \left| x \right| - \frac{{15}}{4}{x^{\frac{4}{3}}} + C = 3\ln \left| x \right| - \frac{{15}}{4}x\sqrt[3]{x} + C\).