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

解

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

- \frac{9 - x ^{2}}{3 x ^{3}} + \frac{9 - x ^{2}}{27 x} + C

解答ステップ

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

部分積分を適用する

= - \frac{9 - x ^{2}}{3 x ^{3}} - \int \frac{1}{3 x ^{2} - x ^{2} + 9} d x

\int \frac{1}{3 x ^{2} - x ^{2} + 9} d x = - \frac{9 - x ^{2}}{27 x}

= - \frac{9 - x ^{2}}{3 x ^{3}} - (- \frac{9 - x ^{2}}{27 x})

簡素化

= - \frac{9 - x ^{2}}{3 x ^{3}} + \frac{9 - x ^{2}}{27 x}

定数を解答に追加する

= - \frac{9 - x ^{2}}{3 x ^{3}} + \frac{9 - x ^{2}}{27 x} + C