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

解答

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

sin (x) (x + 1) + cos (x) + C

求解步骤

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

使用分布积分法

= sin (x) (x + 1) - \int sin (x) d x

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

= sin (x) (x + 1) - (- cos (x))

化简

= sin (x) (x + 1) + cos (x)

解答补常数

= sin (x) (x + 1) + cos (x) + C

\int 2 x^{- 3} + \frac{1}{x} - \frac{4}{1 - x ^{2}} d x

\int e^{- x} \cdot arccot (e^{x}) d x

\int x^{2} (x^{3} - 1)^{5} d x

\int 2 x^{3} y^{4} + x d x

\int (sin (x))^{3} (cos (x))^{5} d x