integral of (sqrt(49x^2-100))/(x^3)

解

\int \frac{49 x ^{2} - 100}{x ^{3}} d x

- \frac{49 x ^{2} - 100}{2 x ^{2}} + \frac{49}{20} arcsec (\frac{7}{10} x) + C

解答ステップ

\int \frac{49 x ^{2} - 100}{x ^{3}} d x

部分積分を適用する

= - \frac{49 x ^{2} - 100}{2 x ^{2}} - \int - \frac{49}{2 x 49 x ^{2} - 100} d x

\int - \frac{49}{2 x 49 x ^{2} - 100} d x = - \frac{49}{20} arcsec (\frac{7}{10} x)

= - \frac{49 x ^{2} - 100}{2 x ^{2}} - (- \frac{49}{20} arcsec (\frac{7}{10} x))

簡素化

= - \frac{49 x ^{2} - 100}{2 x ^{2}} + \frac{49}{20} arcsec (\frac{7}{10} x)

定数を解答に追加する

= - \frac{49 x ^{2} - 100}{2 x ^{2}} + \frac{49}{20} arcsec (\frac{7}{10} x) + C