integral from 1 to 5 of 4/x

解答

\int_{1}^{5} \frac{4}{x} d x

4 ln (5)

十进制

6.43775 \dots

求解步骤

\int_{1}^{5} \frac{4}{x} d x

提出常数:

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

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

使用积分常见定则:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 [ln ∣ x ∣]_{1}^{5}

带入上下限计算后得:

ln (5)

= 4 ln (5)

n = 1 \sum \infty \frac{2}{3 ^{n} + 1}

y^{^{'}} = (1 - 2 x) y^{2}, y (0) = - \frac{1}{30}

\int_{0}^{8} k (8 - x)

d er i v a t i v e f (x) = - 6 x^{2} + 7 x

t an g e n t f (x) = - 1 - 4 e^{- \frac{x}{3}}, at x = 8