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[tex]\displaystyle\bf\\1)\\\\f(x)=x^{\frac{3}{4} } \\\\F(x)=\frac{4}{7} x^{\frac{7}{4} } +C\\\\\\F(x)=\frac{4}{7} \sqrt[4]{x^{7} } +C\\\\\\\boxed{F(x)=\frac{4}{7} x\sqrt[4]{x^{3} } +C}\\\\\\2)\\\\f(x)=x\sqrt{x} =x\cdot x^{\frac{1}{2} } =x^{\frac{3}{2} } \\\\\\F(x)=\frac{2}{5} x^{\frac{5}{2} } +C\\\\\\F(x)=\frac{2}{5} \sqrt{x^{5} } +C\\\\\\\boxed{F(x)=\frac{2}{5} x^{2} \sqrt{x} +C}\\\\3)[/tex]

[tex]\displaystyle\bf\\f(x)=\frac{1}{x^{2} \sqrt{x} } =\frac{1}{x^{2} \cdot x^{\frac{1}{2} } }=\frac{1}{x^{\frac{5}{2} } } =x^{-\frac{5}{2} } \\\\\\F(x)=-\frac{2}{3} x^{-\frac{3}{2} } +C\\\\\\F(x)=-\frac{2}{3} \cdot \frac{1}{x^{\frac{3}{2} } } +C\\\\\\\boxed{F(x)=-\frac{2}{3x\sqrt{x} } +C}[/tex]