integral of (x^{3/2}-2x^6-1.2)/x

解答

\int \frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} d x

0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣ + C

求解步骤

\int \frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} d x

乘开

\frac{x ^{\frac{3}{2}} - 2 x ^{6} - 1.2}{x} : x^{\frac{1}{2}} - 2 x^{5} - \frac{1.2}{x}

= \int x^{\frac{1}{2}} - 2 x^{5} - \frac{1.2}{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 x^{\frac{1}{2}} d x - \int 2 x^{5} d x - \int \frac{1.2}{x} d x

\int x^{\frac{1}{2}} d x = \frac{2}{3} x^{\frac{3}{2}}

\int 2 x^{5} d x = \frac{x ^{6}}{3}

\int \frac{1.2}{x} d x = 1.2 ln ∣ x ∣

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{6}}{3} - 1.2 ln ∣ x ∣

化简

= 0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣

解答补常数

= 0.66666 \dots x^{\frac{3}{2}} - 0.33333 \dots x^{6} - 1.2 ln ∣ x ∣ + C

\int \frac{x ^{2} - x + 2}{x ^{3} + x} d x

x \to 0 - lim (\frac{14 x ^{4} - 14 x}{x})

\frac{\partial}{\partial x} (x^{3} y + sin (x y))

\frac{d}{d x} (3 x^{2} - 4 x - 5)

in v erse l a pl a ce \frac{( - s - 1 )}{s ^{2} + s + 1}