integral of sec(x/5)

解答

\int sec (\frac{x}{5}) d x

5 ln tan (\frac{x}{5}) + sec (\frac{x}{5}) + C

求解步骤

\int sec (\frac{x}{5}) d x

使用换元积分法

= \int sec (u) \cdot 5 d u

提出常数:

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

= 5 \cdot \int sec (u) d u

使用积分常见定则:

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

= 5 ln ∣ tan (u) + sec (u) ∣

u = \frac{x}{5}

代回

= 5 ln tan (\frac{x}{5}) + sec (\frac{x}{5})

解答补常数

= 5 ln tan (\frac{x}{5}) + sec (\frac{x}{5}) + C

in v erse l a pl a ce \frac{1}{s ( s ^{2} + 5 s + 6 )}

x \to 0 lim (x sin (\frac{1}{x ^{2}}))

d er i v a t i v e f (x) = \frac{x}{x - 1}

f (x) = 6^{x}

\int \frac{1}{x ^{2} 25 + x ^{2}} d x