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** Step-by-step Solution **

Problem to solve:

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Expand the integral $\int\left(x^2\sqrt{6x^3}+5\right)dx$ into $2$ integrals using the sum rule for integrals, to then solve each integral separately

Learn how to solve integrals with radicals problems step by step online.

$\int x^2\sqrt{6x^3}dx+\int5dx$

Learn how to solve integrals with radicals problems step by step online. Integrate int(x^2(6x^3)^1/2+5)dx. Expand the integral \int\left(x^2\sqrt{6x^3}+5\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int x^2\sqrt{6x^3}dx results in: \frac{4}{3\sqrt{6}}\sqrt{x^{9}}. The integral \int5dx results in: 5x. Gather the results of all integrals.

** Final Answer

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