integral of 9xcos(x)

解答

\int 9 x cos (x) d x

9 (x sin (x) + cos (x)) + C

求解步骤

\int 9 x cos (x) d x

提出常数:

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

= 9 \cdot \int x cos (x) d x

使用分布积分法

= 9 (x sin (x) - \int sin (x) d x)

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

= 9 (x sin (x) - (- cos (x)))

化简

= 9 (x sin (x) + cos (x))

解答补常数

= 9 (x sin (x) + cos (x)) + C

\frac{d y}{d x} = \frac{1}{y}

d er i v a t i v e f (x) = x^{3} (x - 8)^{2}

\frac{d y}{d x} = e^{2 y} sin (3 x)

t an g e n t f (x) = \frac{7}{x}, at x = 1

\frac{\partial}{\partial x} ((x)^{2} y)