\(\int\left(\sqrt[4]{x^3}+\sqrt[3]{x}+3\sqrt{x}\right)dx\)
\(=\int\left(x^{\frac{3}{4}}+x^{\frac{1}{3}}+3x^{\frac{1}{2}}\right)dx\)
\(=\int x^{\frac{3}{4}}.dx+\int x^{\frac{1}{3}}.dx+3\int x^{\frac{1}{2}}.dx\)
\(=\frac{4}{7}x^{\frac{7}{4}}+\frac{3}{4}x^{\frac{4}{3}}+2.x^{\frac{3}{2}}+C\)