Question

\(\int\sqrt{x}\left(2x-3\sqrt[3]{x^2}-1\right)dx\)

Answer 1

Lời giải:
\(I=\int \sqrt{x}(2x-3\sqrt[3]{x^2}-1)dx=\int x^{\frac{1}{2}}(2x-3x^{\frac{2}{3}}-1)dx\)

\(=2\int x^{\frac{3}{2}}dx-3\int x^{\frac{7}{6}}dx-\int x^{\frac{1}{2}}dx\)

\(=2.\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}-3.\frac{x^{\frac{7}{6}+1}}{\frac{7}{6}+1}-\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C\)

\(=\frac{4}{5}x^{\frac{5}{2}}-\frac{18}{13}x^{\frac{13}{6}}-\frac{2}{3}x^{\frac{3}{2}}+C\)