integral of (-1)^nx^n

解答

\int (- 1)^{n} x^{n} d x

\frac{( - 1 ) ^{n} x ^{n + 1}}{n + 1} + C

求解步骤

\int (- 1)^{n} x^{n} d x

提出常数:

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

= (- 1)^{n} \cdot \int x^{n} d x

使用幂法则

= (- 1)^{n} \frac{x ^{n + 1}}{n + 1}

分式相乘:

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

= \frac{( - 1 ) ^{n} x ^{n + 1}}{n + 1}

解答补常数

= \frac{( - 1 ) ^{n} x ^{n + 1}}{n + 1} + C

\int y^{3} (2 y^{2} - 3) d y

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

\frac{d x}{d t} = - 3 x

h \to 0 lim (\frac{e ^{2 h} - 1}{h})

t an g e n t f (x) = 2 x 5 - 2 x, at x = - 1