integral of (rivative of cos(2x))^2

解答

\int (\frac{d}{d x} (cos (2 x)))^{2} d x

\frac{d}{d x} (cos (2 x))^{2} x - 8 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

求解步骤

\int \frac{d}{d x} (cos (2 x))^{2} d x

使用分布积分法

= \frac{d}{d x} (cos (2 x))^{2} x - \int 8 sin (4 x) x d x

\int 8 sin (4 x) x d x = 8 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

= \frac{d}{d x} (cos (2 x))^{2} x - 8 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x))

解答补常数

= \frac{d}{d x} (cos (2 x))^{2} x - 8 (- \frac{1}{4} x cos (4 x) + \frac{1}{16} sin (4 x)) + C

f a c t or x - x e^{5 x + 2}

f a c t or m x^{2} - p x^{2} + p a^{2} - m a^{2}

f a c t or 3^{12} \cdot 7

f a c t or x + 3 - 4

f a c t or f (x) (x^{2} - 1)^{l n (x^{2} - 1)}