What is the integral of (sqrt(25-9x^2))/(x^2) ?

The integral of (sqrt(25-9x^2))/(x^2) is -(sqrt(25-9x^2))/x-3arcsin(3/5 x)+C

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integral of (sqrt(25-9x^2))/(x^2)

\int \frac{25 - 9 x ^{2}}{x ^{2}} d x

- \frac{25 - 9 x ^{2}}{x} - 3 arcsin (\frac{3}{5} x) + C

Solution steps

\int \frac{25 - 9 x ^{2}}{x ^{2}} d x

Apply Integration By Parts

: - \frac{25 - 9 x ^{2}}{x} - \int \frac{9}{25 - 9 x ^{2}} d x

= - \frac{25 - 9 x ^{2}}{x} - \int \frac{9}{25 - 9 x ^{2}} d x

\int \frac{9}{25 - 9 x ^{2}} d x = 3 arcsin (\frac{3}{5} x)

= - \frac{25 - 9 x ^{2}}{x} - 3 arcsin (\frac{3}{5} x)

Add a constant to the solution

= - \frac{25 - 9 x ^{2}}{x} - 3 arcsin (\frac{3}{5} x) + C

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What is the integral of (sqrt(25-9x^2))/(x^2) ?
The integral of (sqrt(25-9x^2))/(x^2) is -(sqrt(25-9x^2))/x-3arcsin(3/5 x)+C