integral of e^xx-e^x

解答

\int e^{x} x - e^{x} d x

e^{x} x - 2 e^{x} + C

求解步骤

\int e^{x} x - e^{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 e^{x} x d x - \int e^{x} d x

\int e^{x} x d x = e^{x} x - e^{x}

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

= e^{x} x - e^{x} - e^{x}

化简

= e^{x} x - 2 e^{x}

解答补常数

= e^{x} x - 2 e^{x} + C

x \to 5 lim (x^{3})

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

y^{^{''}} - y^{^{'}} - 2 y = 7 e^{- t}

\frac{\partial}{\partial x} (7 x y^{6})

x \to 0 lim (\frac{x - 8}{x - 1})