integral of sin(5x)

解答

\int sin (5 x) d x

- \frac{1}{5} cos (5 x) + C

求解步骤

\int sin (5 x) d x

使用换元积分法

= \int sin (u) \frac{1}{5} d u

提出常数:

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

= \frac{1}{5} \cdot \int sin (u) d u

使用积分常见定则:

\int sin (u) d u = - cos (u)

= \frac{1}{5} (- cos (u))

u = 5 x

代回

= \frac{1}{5} (- cos (5 x))

化简

= - \frac{1}{5} cos (5 x)

解答补常数

= - \frac{1}{5} cos (5 x) + C

d er i v a t i v e 4 t - 4 e^{t}

d er i v a t i v e f (x) = cos (6 x) \cdot 6

\int x sin (x + y) d x

\frac{d}{d x} (e^{x s e c (x)})

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