integral of 1/(cos(x-1))

解答

\int \frac{1}{cos ( x - 1 )} d x

ln ∣ tan (x - 1) + sec (x - 1) ∣ + C

求解步骤

\int \frac{1}{cos ( x - 1 )} d x

使用三角恒等式改写

= \int sec (x - 1) d x

使用换元积分法

= \int sec (u) d u

使用积分常见定则:

\int sec (u) d u = ln ∣ tan (u) + sec (u) ∣

= ln ∣ tan (u) + sec (u) ∣

u = x - 1

代回

= ln ∣ tan (x - 1) + sec (x - 1) ∣

解答补常数

= ln ∣ tan (x - 1) + sec (x - 1) ∣ + C

d er i v a t i v e f (x) = x^{3} - 2 x

a re a 4 x + 10, x^{2} + 6 x + 6, - 2, 2

(x^{2} + 16) \frac{d y}{d x} + x y = 5 x

d er i v a t i v e lo g_{8} (5 x^{3} + 3 x)

\int_{0}^{2} (1 + x^{2}) d x