What is the integral of (x^2)/((9-y^2)^{5/2)} ?

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

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integral of (x^2)/((9-y^2)^{5/2)}

\int \frac{x ^{2}}{( 9 - y ^{2} ) ^{\frac{5}{2}}} d x

\frac{x ^{3}}{3 ( 9 - y ^{2} ) ^{\frac{5}{2}}} + C

Solution steps

\int \frac{x ^{2}}{( 9 - y ^{2} ) ^{\frac{5}{2}}} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{( 9 - y ^{2} ) ^{\frac{5}{2}}} \cdot \int x^{2} d x

Apply the Power Rule

: \frac{x ^{3}}{3}

= \frac{1}{( 9 - y ^{2} ) ^{\frac{5}{2}}} \cdot \frac{x ^{3}}{3}

Simplify

\frac{1}{( 9 - y ^{2} ) ^{\frac{5}{2}}} \cdot \frac{x ^{3}}{3} : \frac{x ^{3}}{3 ( 9 - y ^{2} ) ^{\frac{5}{2}}}

= \frac{x ^{3}}{3 ( 9 - y ^{2} ) ^{\frac{5}{2}}}

Add a constant to the solution

= \frac{x ^{3}}{3 ( 9 - y ^{2} ) ^{\frac{5}{2}}} + C

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