What is the integral of xsqrt(4-x^2)-x^2(sqrt(3))/3 ?

The integral of xsqrt(4-x^2)-x^2(sqrt(3))/3 is -1/3 (4-x^2)^{3/2}-(x^3)/(3sqrt(3))+C

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integral of xsqrt(4-x^2)-x^2(sqrt(3))/3

\int x 4 - x^{2} - x^{2} \frac{3}{3} d x

- \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3 3} + C

Solution steps

\int x 4 - x^{2} - x^{2} \frac{3}{3} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x 4 - x^{2} d x - \int x^{2} \frac{3}{3} d x

\int x 4 - x^{2} d x = - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}}

\int x^{2} \frac{3}{3} d x = \frac{x ^{3}}{3 3}

= - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3 3}

Add a constant to the solution

= - \frac{1}{3} (4 - x^{2})^{\frac{3}{2}} - \frac{x ^{3}}{3 3} + C

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What is the integral of xsqrt(4-x^2)-x^2(sqrt(3))/3 ?
The integral of xsqrt(4-x^2)-x^2(sqrt(3))/3 is -1/3 (4-x^2)^{3/2}-(x^3)/(3sqrt(3))+C