integral of cot(t)

解答

\int cot (t) d t

ln ∣ sin (t) ∣ + C

求解步骤

\int cot (t) d t

使用三角恒等式改写

= \int \frac{cos ( t )}{sin ( t )} d t

使用换元积分法

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

使用积分常见定则:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

u = sin (t)

代回

= ln ∣ sin (t) ∣

解答补常数

= ln ∣ sin (t) ∣ + C

x \to - 2 lim (\frac{1}{x + 2})

\int sec^{2} (1 - 4 x) d x

\frac{d y}{d x} = e^{x - y}, y (0) = ln (8)

x \to 0 lim ((1 + 6 x)^{\frac{3}{x}})

in v erse l a pl a ce \frac{1}{s ^{3} + s}