integral of (x+1)sin(3x)

解答

\int (x + 1) sin (3 x) d x

- \frac{1}{3} cos (3 x) (x + 1) + \frac{1}{9} sin (3 x) + C

求解步骤

\int (x + 1) sin (3 x) d x

使用分布积分法

= - \frac{1}{3} cos (3 x) (x + 1) - \int - \frac{1}{3} cos (3 x) d x

\int - \frac{1}{3} cos (3 x) d x = - \frac{1}{9} sin (3 x)

= - \frac{1}{3} cos (3 x) (x + 1) - (- \frac{1}{9} sin (3 x))

化简

= - \frac{1}{3} cos (3 x) (x + 1) + \frac{1}{9} sin (3 x)

解答补常数

= - \frac{1}{3} cos (3 x) (x + 1) + \frac{1}{9} sin (3 x) + C

\frac{d}{d x} (\frac{( x + 3 ) ( x + 1 )}{x ^{2} - 49})

\int_{0}^{1} x cos (π x) d x

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

l a pl a ce t r an s f or m t^{2} e^{- 2 t} sin (3 t + 30)

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