Final answer to the problem
$\frac{36\sqrt[3]{x^{2}}}{7}-\frac{24}{7}x^{-\frac{7}{2}}-\frac{9}{44}\sqrt{x^{11}}+C_0$
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Step-by-step Solution
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1
Rewrite the integrand $\frac{3}{2\sqrt{x}}\left(\frac{6}{7\sqrt[4]{x}}+\frac{8}{x^4}+\frac{-3x^5}{4}\right)$ in expanded form
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$\int\frac{3\left(24\sqrt[4]{x^{15}}+224-21x^{9}\right)}{56\sqrt{x^{9}}}dx$
Learn how to solve problems step by step online. Integrate int(3/(2x^(1/2))(6/(7x^(1/4))+8/(x^4)(-3x^5)/4))dx. Rewrite the integrand \frac{3}{2\sqrt{x}}\left(\frac{6}{7\sqrt[4]{x}}+\frac{8}{x^4}+\frac{-3x^5}{4}\right) in expanded form. Take out the constant 3 from the integral. Take the constant \frac{1}{56} out of the integral. Multiply the fraction and term in 3\cdot \left(\frac{1}{56}\right)\int\frac{24\sqrt[4]{x^{15}}+224-21x^{9}}{\sqrt{x^{9}}}dx.
Final answer to the problem
$\frac{36\sqrt[3]{x^{2}}}{7}-\frac{24}{7}x^{-\frac{7}{2}}-\frac{9}{44}\sqrt{x^{11}}+C_0$
