What is the integral of (sqrt(-9x^2+4))/(x^2) ?

The integral of (sqrt(-9x^2+4))/(x^2) is -(sqrt(-9x^2+4))/x-3arcsin(3/2 x)+C

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integral of (sqrt(-9x^2+4))/(x^2)

\int \frac{- 9 x ^{2} + 4}{x ^{2}} d x

- \frac{- 9 x ^{2} + 4}{x} - 3 arcsin (\frac{3}{2} x) + C

Solution steps

\int \frac{- 9 x ^{2} + 4}{x ^{2}} d x

Apply Integration By Parts

: - \frac{- 9 x ^{2} + 4}{x} - \int \frac{9}{- 9 x ^{2} + 4} d x

= - \frac{- 9 x ^{2} + 4}{x} - \int \frac{9}{- 9 x ^{2} + 4} d x

\int \frac{9}{- 9 x ^{2} + 4} d x = 3 arcsin (\frac{3}{2} x)

= - \frac{- 9 x ^{2} + 4}{x} - 3 arcsin (\frac{3}{2} x)

Add a constant to the solution

= - \frac{- 9 x ^{2} + 4}{x} - 3 arcsin (\frac{3}{2} x) + C

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What is the integral of (sqrt(-9x^2+4))/(x^2) ?
The integral of (sqrt(-9x^2+4))/(x^2) is -(sqrt(-9x^2+4))/x-3arcsin(3/2 x)+C