integral from 0 to 1 of 1/(x-3)

解答

\int_{0}^{1} \frac{1}{x - 3} d x

ln (2) - ln (3)

十进制

- 0.40546 \dots

求解步骤

\int_{0}^{1} \frac{1}{x - 3} d x

使用换元积分法

= \int_{- 3}^{- 2} \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{- 3}^{- 2}

带入上下限计算后得:

ln (2) - ln (3)

= ln (2) - ln (3)

y^{^{''}} - 81 y = 0, y (2) = 2, y (- 1) = - 1

\frac{d}{d x} (x + e)

d er i v a t i v e \frac{1}{sin ( x ) cos ( x + b + c )}

\int_{0}^{1} arcsin (x) - sin (x) d x

\int (\frac{3 x ^{2} + 3 x + 1}{x}) d x