Final Answer
$-\frac{8}{243}\sqrt{4-9x^2}+\frac{-\left(3x\right)^{2}\sqrt{4-9x^2}}{243}+\frac{1}{2}x^2+C_0$
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Step-by-step Solution
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Simplifying
$\int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx$
Learn how to solve integrals of polynomial functions problems step by step online.
$\int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx$
Learn how to solve integrals of polynomial functions problems step by step online. Integrate int((x^3)/((4+1*-9x^2)^1/2)+x)dx. Simplifying. Expand the integral \int\left(\frac{x^3}{\sqrt{4-9x^2}}+x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x^3}{\sqrt{4-9x^2}}dx results in: \frac{-\left(3x\right)^{2}\sqrt{4-9x^2}}{243}-\frac{8}{243}\sqrt{4-9x^2}. Gather the results of all integrals.
Final Answer
$-\frac{8}{243}\sqrt{4-9x^2}+\frac{-\left(3x\right)^{2}\sqrt{4-9x^2}}{243}+\frac{1}{2}x^2+C_0$