integral of ((5x^3-3)/x)

解答

\int (\frac{5 x ^{3} - 3}{x}) d x

\frac{5 x ^{3}}{3} - 3 ln ∣ x ∣ + C

求解步骤

\int \frac{5 x ^{3} - 3}{x} d x

乘开

\frac{5 x ^{3} - 3}{x} : 5 x^{2} - \frac{3}{x}

= \int 5 x^{2} - \frac{3}{x} 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 5 x^{2} d x - \int \frac{3}{x} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int \frac{3}{x} d x = 3 ln ∣ x ∣

= \frac{5 x ^{3}}{3} - 3 ln ∣ x ∣

解答补常数

= \frac{5 x ^{3}}{3} - 3 ln ∣ x ∣ + C

in v erse l a pl a ce \frac{8.75}{S + \frac{2}{3}}

\frac{d}{d x} (\frac{2 x + 5}{x ^{2} + 5 x})

\int \frac{11}{( t ^{2} + 1 ) ^{\frac{3}{2}}} d t

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

t an g e n t f (x) = 3^{x}, at x = 1