integral of 2x+2x^{-2}

解答

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

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

求解步骤

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

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

= \int 2 x + \frac{2}{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 2 x d x + \int \frac{2}{x ^{2}} d x

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

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

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

解答补常数

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

\int \frac{x}{6 + π} d x

\frac{d}{d x} ((x^{2}) \cdot ln (x))

d er i v a t i v e f (x) = \frac{x ^{2}}{9 + 2 x}

\int_{0}^{1} π (x - x^{10}) d x

\frac{d}{d x} (3 x^{2} e^{x} + x^{3} e^{x})