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

解答

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

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

求解步骤

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

使用分布积分法

= - \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)

解答补常数

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

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