integral of ((11)/x+x/(11))

解答

\int (\frac{11}{x} + \frac{x}{11}) d x

11 ln ∣ x ∣ + \frac{x ^{2}}{22} + C

求解步骤

\int \frac{11}{x} + \frac{x}{11} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int \frac{11}{x} d x + \int \frac{x}{11} d x

\int \frac{11}{x} d x = 11 ln ∣ x ∣

\int \frac{x}{11} d x = \frac{x ^{2}}{22}

= 11 ln ∣ x ∣ + \frac{x ^{2}}{22}

解答补常数

= 11 ln ∣ x ∣ + \frac{x ^{2}}{22} + C

y^{^{''}} - 14 y^{^{'}} + 53 y = 0

\int 20 cos (10 t + \frac{π}{6}) + 2 d t

d er i v a t i v e f (x) = - 6 x

\frac{d}{d x} (6 (x^{2} + 4)^{8})

\frac{d}{d x} (\frac{π x}{3})