integral of 4/(x^5)

解答

\int \frac{4}{x ^{5}} d x

- \frac{1}{x ^{4}} + C

求解步骤

\int \frac{4}{x ^{5}} d x

提出常数:

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

= 4 \cdot \int \frac{1}{x ^{5}} d x

使用幂法则

= 4 (- \frac{1}{4 x ^{4}})

化简

4 (- \frac{1}{4 x ^{4}}) : - \frac{1}{x ^{4}}

= - \frac{1}{x ^{4}}

解答补常数

= - \frac{1}{x ^{4}} + C

\frac{d}{d x} (\frac{4 x + 6}{x + 3})

\frac{d}{d x} (3^{x} ln (x))

\int \frac{4 x ^{2} - 25}{x ^{3}} d x

\frac{d}{d x} (3 e^{x} + (x - 2)^{2})

x \to 6 lim (5)