integral of (5/x-3/(x^2))

解答

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

5 ln ∣ x ∣ + \frac{3}{x} + C

求解步骤

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

\int \frac{5}{x} d x = 5 ln ∣ x ∣

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

= 5 ln ∣ x ∣ - (- \frac{3}{x})

化简

= 5 ln ∣ x ∣ + \frac{3}{x}

解答补常数

= 5 ln ∣ x ∣ + \frac{3}{x} + C

\int_{5}^{8} \frac{6}{x - 5} d x

t^{2} y^{^{'}} + y^{2} = t y, y (1) = - \frac{1}{2}

\frac{\partial}{\partial x} (ln (x - y^{2}))

\frac{d y}{d x} = \frac{4 sec ( y )}{( x - 6 ) ^{2}}

\frac{\partial}{\partial x} (x^{2} + x e^{2 y} - y)