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

解答

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

2 x^{2} - \frac{1}{x} - 3 x + C

求解步骤

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

化简

= \int 4 x + \frac{1}{x ^{2}} - 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 4 x d x + \int \frac{1}{x ^{2}} d x - \int 3 d x

\int 4 x d x = 2 x^{2}

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

\int 3 d x = 3 x

= 2 x^{2} - \frac{1}{x} - 3 x

解答补常数

= 2 x^{2} - \frac{1}{x} - 3 x + C

t a y l or \frac{1}{2 x}, 1

\frac{d}{d x} (cos ((ln (x + 1))^{2} - e^{x^{2}}))

\frac{\partial}{\partial x} (2 x^{\frac{1}{2}} y^{\frac{1}{4}})

d er i v a t i v e x^{3} - \frac{x ^{2}}{40}

y^{^{'}} = 4 + 2 sin (\frac{x}{4}) - \frac{y}{100}