integral of 2cos(x)sin(x)+1/(2x)

解答

\int 2 cos (x) sin (x) + \frac{1}{2 x} d x

sin^{2} (x) + \frac{1}{2} ln ∣ x ∣ + C

求解步骤

\int 2 cos (x) sin (x) + \frac{1}{2 x} 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 2 cos (x) sin (x) d x + \int \frac{1}{2 x} d x

\int 2 cos (x) sin (x) d x = sin^{2} (x)

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

= sin^{2} (x) + \frac{1}{2} ln ∣ x ∣

解答补常数

= sin^{2} (x) + \frac{1}{2} ln ∣ x ∣ + C

\int 17 sin^{2} (x) cos^{2} (x) d x

y^{^{'}} - \frac{7}{x} y = \frac{y ^{3}}{x ^{10}}

a re a 75 - 3 x^{2}, [0, 7]

n = 1 \sum \infty n (\frac{7}{8})^{n}

d er i v a t i v e x^{2} + 4 x + 5