integral of 2e^x+8x^3+6x

解答

\int 2 e^{x} + 8 x^{3} + 6 x d x

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

求解步骤

\int 2 e^{x} + 8 x^{3} + 6 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 2 e^{x} d x + \int 8 x^{3} d x + \int 6 x d x

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

\int 8 x^{3} d x = 2 x^{4}

\int 6 x d x = 3 x^{2}

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

解答补常数

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

\frac{d y}{d x} + 3 y = 8

\int_{2}^{3} \frac{9}{3 - x} d x

\frac{d}{d x} (x^{4} - 4 x^{3} + 10)

x \to 0 lim (8 e^{x} sin (x))

\frac{1}{4} y^{^{''}} + 10 y^{^{'}} + 1000 y = 0