integral of (sqrt(36x^2-49))/(x^3)

解答

\int \frac{36 x ^{2} - 49}{x ^{3}} d x

- \frac{36 x ^{2} - 49}{2 x ^{2}} + \frac{18}{7} arcsec (\frac{6}{7} x) + C

求解步骤

\int \frac{36 x ^{2} - 49}{x ^{3}} d x

使用分布积分法

= - \frac{36 x ^{2} - 49}{2 x ^{2}} - \int - \frac{18}{x 36 x ^{2} - 49} d x

\int - \frac{18}{x 36 x ^{2} - 49} d x = - \frac{18}{7} arcsec (\frac{6}{7} x)

= - \frac{36 x ^{2} - 49}{2 x ^{2}} - (- \frac{18}{7} arcsec (\frac{6}{7} x))

化简

= - \frac{36 x ^{2} - 49}{2 x ^{2}} + \frac{18}{7} arcsec (\frac{6}{7} x)

解答补常数

= - \frac{36 x ^{2} - 49}{2 x ^{2}} + \frac{18}{7} arcsec (\frac{6}{7} x) + C

x \to \frac{π}{2} - lim (sec (x))

t an g e n t - 9 x^{\frac{1}{3}} + 5, at x = 27

\int + (x^{2} - 1) d x

d er i v a t i v e 5 u

x \to 3 lim (x^{2} + 3)