What is the integral from x^3 to sqrt(x of)x^2+3y^2 ?

The integral from x^3 to sqrt(x of)x^2+3y^2 is x^2sqrt(x)-x^5+x^{3/2}-x^9

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integral from x^3 to sqrt(x of)x^2+3y^2

\int_{x^{3}}^{x} x^{2} + 3 y^{2} d y

x^{2} x - x^{5} + x^{\frac{3}{2}} - x^{9}

Solution steps

\int_{x^{3}}^{x} x^{2} + 3 y^{2} d y

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^{3}}^{x} x^{2} d y + \int_{x^{3}}^{x} 3 y^{2} d y

\int_{x^{3}}^{x} x^{2} d y = x^{2} x - x^{5}

\int_{x^{3}}^{x} 3 y^{2} d y = x^{\frac{3}{2}} - x^{9}

= x^{2} x - x^{5} + x^{\frac{3}{2}} - x^{9}

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What is the integral from x^3 to sqrt(x of)x^2+3y^2 ?
The integral from x^3 to sqrt(x of)x^2+3y^2 is x^2sqrt(x)-x^5+x^{3/2}-x^9