integral of 1/(1-3t)

解答

\int \frac{1}{1 - 3 t} d t

- \frac{1}{3} ln ∣ 1 - 3 t ∣ + C

求解步骤

\int \frac{1}{1 - 3 t} d t

使用换元积分法

= \int - \frac{1}{3 u} d u

提出常数:

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

= - \frac{1}{3} \cdot \int \frac{1}{u} d u

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - \frac{1}{3} ln ∣ u ∣

u = 1 - 3 t

代回

= - \frac{1}{3} ln ∣ 1 - 3 t ∣

解答补常数

= - \frac{1}{3} ln ∣ 1 - 3 t ∣ + C

y^{^{'}} + 7 y = t + e^{- 5 t}

\frac{\partial}{\partial x} ((n - 1) (\frac{1}{x} - \frac{1}{y}))

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