integral of e^x*7x

解答

\int e^{x} \cdot 7 x d x

7 (e^{x} x - e^{x}) + C

求解步骤

\int e^{x} \cdot 7 x d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int e^{x} x d x

使用分布积分法

= 7 (e^{x} x - \int e^{x} d x)

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

= 7 (e^{x} x - e^{x})

解答补常数

= 7 (e^{x} x - e^{x}) + C

(u^{2} + u) d x + u^{2} (x d u + u d x) = 0

x \to 4 lim (e^{x} + 4 x)

\int 3 2 x d x

\frac{\partial}{\partial x} (7 x sin (5 x^{2} y))

a re a x^{2} = 4 y, 3 x - 4 y + 4 = 0