What is the integral of ((9-x^2)^{1/2})/(x^2) ?

The integral of ((9-x^2)^{1/2})/(x^2) is -((9-x^2)^{1/2})/x-arcsin(1/3 x)+C

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integral of ((9-x^2)^{1/2})/(x^2)

\int \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x ^{2}} d x

- \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x) + C

Solution steps

\int \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x ^{2}} d x

Apply Integration By Parts

: - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - \int \frac{1}{( 9 - x ^{2} ) ^{\frac{1}{2}}} d x

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

\int \frac{1}{( 9 - x ^{2} ) ^{\frac{1}{2}}} d x = arcsin (\frac{1}{3} x)

= - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x)

Add a constant to the solution

= - \frac{( 9 - x ^{2} ) ^{\frac{1}{2}}}{x} - arcsin (\frac{1}{3} x) + C

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What is the integral of ((9-x^2)^{1/2})/(x^2) ?
The integral of ((9-x^2)^{1/2})/(x^2) is -((9-x^2)^{1/2})/x-arcsin(1/3 x)+C