integral of xn(x)

解答

\int x n (x) d x

\frac{n x ^{3}}{3} + C

求解步骤

\int x n x d x

提出常数:

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

= n \cdot \int xx d x

化简

xx : x^{2}

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

使用幂法则

= n \frac{x ^{3}}{3}

分式相乘:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{n x ^{3}}{3}

解答补常数

= \frac{n x ^{3}}{3} + C

\int sec^{13} (x) d x

f (x) = sinh (2 x)

\int_{0}^{l n (2)} e^{x + 2 y} d x

\frac{\partial}{\partial x} (2 x \cdot e^{x y})

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))