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$\displaystyle\int(\sqrt{x}+\sqrt[3]{x} )\, dx\\ =\displaystyle\int\left(x^\tfrac{1}{2}+x^\tfrac{1}{3}\right) \, dx\\ =\dfrac{x^{\tfrac{1}{2}+1}}{\dfrac{2}{3}+1}+\dfrac{x^{\tfrac{1}{3}+1}}{\dfrac{2}{3}+1}+C\\ =\dfrac{2}{3}x^\tfrac{3}{2}+\dfrac{3}{4}x^\tfrac{4}{3}+C\\ =\dfrac{2}{3}x\sqrt{x}+\dfrac{3}{4}x\sqrt[3]{x} +C$
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