integral of (sqrt(25x^2-49))/(x^3)

解答

\int \frac{25 x ^{2} - 49}{x ^{3}} d x

- \frac{25 x ^{2} - 49}{2 x ^{2}} + \frac{25}{14} arcsec (\frac{5}{7} x) + C

求解步骤

\int \frac{25 x ^{2} - 49}{x ^{3}} d x

使用分布积分法

= - \frac{25 x ^{2} - 49}{2 x ^{2}} - \int - \frac{25}{2 x 25 x ^{2} - 49} d x

\int - \frac{25}{2 x 25 x ^{2} - 49} d x = - \frac{25}{14} arcsec (\frac{5}{7} x)

= - \frac{25 x ^{2} - 49}{2 x ^{2}} - (- \frac{25}{14} arcsec (\frac{5}{7} x))

化简

= - \frac{25 x ^{2} - 49}{2 x ^{2}} + \frac{25}{14} arcsec (\frac{5}{7} x)

解答补常数

= - \frac{25 x ^{2} - 49}{2 x ^{2}} + \frac{25}{14} arcsec (\frac{5}{7} x) + C

\frac{d}{d x} (2 x - \frac{2}{x ^{3}})

\int \frac{1 + cos ( x )}{( x + sin ( x ) ) ^{2}} d x

d er i v a t i v e \frac{18}{3 x - 2}

d er i v a t i v e y = x^{6} cos (x)

e^{x} (y^{3} + x y^{3} + 1) d x + 3 y^{2} (x e^{x} - 6) d y = 0