integral of nx^n

解答

\int n x^{n} d x

\frac{n x ^{n + 1}}{n + 1} + C

求解步骤

\int n x^{n} d x

提出常数:

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

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

使用幂法则

= n \frac{x ^{n + 1}}{n + 1}

分式相乘:

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

= \frac{n x ^{n + 1}}{n + 1}

解答补常数

= \frac{n x ^{n + 1}}{n + 1} + C

\int \frac{1}{x ^{2} 3 - x ^{2}} d x

x \to \infty lim (- 2 x)

\frac{2 x ^{4} + 1}{y} \frac{d y}{d x} + \frac{1}{6} y^{3} x^{3} = 0

d er i v a t i v e \frac{1}{2 x}

\int π x^{2} d x