integral of (8e^2x)-(3e^{-x})

解答

\int (8 e^{2} x) - (3 e^{- x}) d x

4 e^{2} x^{2} + 3 e^{- x} + C

求解步骤

\int 8 e^{2} x - 3 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 8 e^{2} x d x - \int 3 e^{- x} d x

\int 8 e^{2} x d x = 4 e^{2} x^{2}

\int 3 e^{- x} d x = - 3 e^{- x}

= 4 e^{2} x^{2} - (- 3 e^{- x})

化简

= 4 e^{2} x^{2} + 3 e^{- x}

解答补常数

= 4 e^{2} x^{2} + 3 e^{- x} + C

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

\frac{d}{d x} (\frac{a + b x}{c + d x})

l a pl a ce t r an s f or m 3 t e^{- 2 t}

\frac{d}{d x} (3 (x - 1)^{2})

\int \frac{1}{sin ^{4} ( x )} d x