integral of (cos(x)-5)

解答

\int (cos (x) - 5) d x

sin (x) - 5 x + C

求解步骤

\int cos (x) - 5 d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (x) d x - \int 5 d x

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

\int 5 d x = 5 x

= sin (x) - 5 x

解答补常数

= sin (x) - 5 x + C

\int \frac{x ^{2} + 2}{x ( x ^{2} + 5 x + 8 )} d x

\int (π sec (x) - tan (x)) sec (x) d x

\int - 6 x sin (3 x^{2} - 1) d x

\int sec (29 w) tan (29 w) d w

\int 11 cos (x) d x