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

解答

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

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

求解步骤

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

使用分布积分法

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

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

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

化简

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

解答补常数

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

\int x^{9} x d x

\int \frac{z ^{2}}{3 2 + z ^{3}} d z

\int (- 3 x^{- 2}) d x

\int \frac{e ^{x}}{e ^{x} - 3} d x

\int \frac{3 x}{x ^{2} + 4 x + 5} d x