Câu 23 :
\(\int\left(\dfrac{\left(1-x\right)^3}{\sqrt[3]{x}}\right)dx=\int\left(\dfrac{1-3x+3x^2-x^3}{x^{\dfrac{1}{3}}}\right)dx\)
\(=\int\left(\dfrac{1}{x^{\dfrac{1}{3}}}-3x^{1-\dfrac{1}{3}}+3x^{2-\dfrac{1}{3}}-x^{3-\dfrac{1}{3}}\right)dx=\int\left(\dfrac{1}{x^{\dfrac{1}{3}}}-3x^{\dfrac{2}{3}}+3x^{\dfrac{5}{3}}-x^{\dfrac{8}{3}}\right)dx\)
\(=\dfrac{x^{-\dfrac{1}{3}+1}}{-\dfrac{1}{3}+1}-3\dfrac{x^{\dfrac{2}{3}+1}}{\dfrac{2}{3}+1}+3\dfrac{x^{\dfrac{5}{3}+1}}{\dfrac{5}{3}+1}-\dfrac{x^{\dfrac{8}{3}+1}}{\dfrac{8}{3}+1}+C\)
\(=\dfrac{3}{2}x^{\dfrac{2}{3}}-\dfrac{9}{5}x^{\dfrac{5}{3}}+\dfrac{9}{8}x^{\dfrac{8}{3}}-\dfrac{3}{11}x^{\dfrac{11}{3}}+C\)
Câu 24 :
\(...=\int\left(x^{\dfrac{2}{3}}-x^{\dfrac{3}{2}}+x^{\dfrac{5}{4}}\right)dx\)
\(=\dfrac{x^{\dfrac{2}{3}+1}}{\dfrac{2}{3}+1}-\dfrac{x^{\dfrac{3}{2}+1}}{\dfrac{3}{2}+1}+\dfrac{x^{\dfrac{5}{4}+1}}{\dfrac{5}{4}+1}+C\)
\(=\dfrac{3}{5}x^{\dfrac{5}{3}}-\dfrac{2}{5}x^{\dfrac{5}{2}}+\dfrac{4}{9}x^{\dfrac{9}{4}}+C\)
giúp em với, khoảng sáng mai nộp ạ. Cảm ưn mn nha ^^