integral of 3/x+10x-3

解答

\int \frac{3}{x} + 10 x - 3 d x

3 ln ∣ x ∣ + 5 x^{2} - 3 x + C

求解步骤

\int \frac{3}{x} + 10 x - 3 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{3}{x} d x + \int 10 x d x - \int 3 d x

\int \frac{3}{x} d x = 3 ln ∣ x ∣

\int 10 x d x = 5 x^{2}

\int 3 d x = 3 x

= 3 ln ∣ x ∣ + 5 x^{2} - 3 x

解答补常数

= 3 ln ∣ x ∣ + 5 x^{2} - 3 x + C

\int_{1}^{2} \frac{7 ln ( x )}{x ^{2}} d x

\int 5 x \cdot 3 1 - x^{2} d x

\frac{\partial}{\partial x} (\frac{1}{1 - b x})

\frac{d}{d x} ((2 x - 7)^{4} (x^{2} + x + 1)^{5})

y^{^{''}} + y^{^{'}} - 2 y = 0, y (0) = 0, y^{^{'}} (0) = 1