integral of (x^3)/(1-9x^2)

解答

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

- \frac{x ^{2}}{18} - \frac{1}{162} ln - 9 x^{2} + 1 + C

求解步骤

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

长除

\frac{x ^{3}}{1 - 9 x ^{2}} : - \frac{x}{9} + \frac{x}{9 ( - 9 x ^{2} + 1 )}

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

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int \frac{x}{9} d x = \frac{x ^{2}}{18}

\int \frac{x}{9 ( - 9 x ^{2} + 1 )} d x = - \frac{1}{162} ln - 9 x^{2} + 1

= - \frac{x ^{2}}{18} - \frac{1}{162} ln - 9 x^{2} + 1

解答补常数

= - \frac{x ^{2}}{18} - \frac{1}{162} ln - 9 x^{2} + 1 + C

d er i v a t i v e y = \frac{x + 7}{5 x ^{2} e ^{x}}

\int (\frac{4}{x} + e^{2 x}) d x

\int sec (x) sec^{2} (x) d x

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

x \to 2 lim (\frac{x ^{2} - 6}{x - 3})