integral of (sqrt(w^2-25))/(w^3)

解答

\int \frac{w ^{2} - 25}{w ^{3}} d w

- \frac{w ^{2} - 25}{2 w ^{2}} + \frac{1}{10} arcsec (\frac{1}{5} w) + C

求解步骤

\int \frac{w ^{2} - 25}{w ^{3}} d w

使用分布积分法

= - \frac{w ^{2} - 25}{2 w ^{2}} - \int - \frac{1}{2 w w ^{2} - 25} d w

\int - \frac{1}{2 w w ^{2} - 25} d w = - \frac{1}{10} arcsec (\frac{1}{5} w)

= - \frac{w ^{2} - 25}{2 w ^{2}} - (- \frac{1}{10} arcsec (\frac{1}{5} w))

化简

= - \frac{w ^{2} - 25}{2 w ^{2}} + \frac{1}{10} arcsec (\frac{1}{5} w)

解答补常数

= - \frac{w ^{2} - 25}{2 w ^{2}} + \frac{1}{10} arcsec (\frac{1}{5} w) + C

l a pl a ce t r an s f or m 0.03 \cdot (1 - cos (2 t))

x \to 0 lim ((2 x^{2})^{x^{4}})

\frac{d}{d n} ((lo g_{10} (n))^{3})

\int \frac{1}{y ( 2 - y )} d y

d er i v a t i v e f (x) = ln (\frac{1 - x}{1 + x})