Final answer to the problem
$\frac{8}{9}\sqrt[4]{v^{9}}+\frac{24}{5}\sqrt[4]{v^{5}}+\frac{-1}{v^{3}}+C_0$
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Step-by-step Solution
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Simplifying
$\int\left(2\sqrt[4]{v^{5}}+6\sqrt[4]{v}+3v^{-4}\right)dv$
Learn how to solve differential equations problems step by step online.
$\int\left(2\sqrt[4]{v^{5}}+6\sqrt[4]{v}+3v^{-4}\right)dv$
Learn how to solve differential equations problems step by step online. Integrate int(2v^(5/4)+6v^1/43v^(-4))dv. Simplifying. Expand the integral \int\left(2\sqrt[4]{v^{5}}+6\sqrt[4]{v}+3v^{-4}\right)dv into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2\sqrt[4]{v^{5}}dv results in: \frac{8}{9}\sqrt[4]{v^{9}}. The integral \int6\sqrt[4]{v}dv results in: \frac{24}{5}\sqrt[4]{v^{5}}.
Final answer to the problem
$\frac{8}{9}\sqrt[4]{v^{9}}+\frac{24}{5}\sqrt[4]{v^{5}}+\frac{-1}{v^{3}}+C_0$