integral of 3x^24x^4

解答

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

\frac{12 x ^{7}}{7} + C

求解步骤

\int 3 x^{2} \cdot 4 x^{4} d x

提出常数:

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

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

化简

= 12 \cdot \int x^{2} x^{4} d x

化简

x^{2} x^{4} : x^{6}

= 12 \cdot \int x^{6} d x

使用幂法则

= 12 \cdot \frac{x ^{7}}{7}

分式相乘:

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

= \frac{12 x ^{7}}{7}

解答补常数

= \frac{12 x ^{7}}{7} + C

x \to 0 lim (4 - 5 x)

d er i v a t i v e f (x) = x^{2} - 5, c = 3

\int_{- 2}^{3} \frac{24}{x ^{4}} d x

x y^{^{'}} - 3 y^{2} = 0, y (e) = 1

\int - e^{2 x} sin (e^{x}) d x