What is the integral of 21xcos(3x)-8sin(3x) ?

The integral of 21xcos(3x)-8sin(3x) is 7xsin(3x)+5cos(3x)+C

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integral of 21xcos(3x)-8sin(3x)

\int 21 x cos (3 x) - 8 sin (3 x) d x

7 x sin (3 x) + 5 cos (3 x) + C

Solution steps

\int 21 x cos (3 x) - 8 sin (3 x) d x

Apply the Sum Rule:

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

= \int 21 x cos (3 x) d x - \int 8 sin (3 x) d x

\int 21 x cos (3 x) d x = 7 x sin (3 x) + \frac{7}{3} cos (3 x)

\int 8 sin (3 x) d x = - \frac{8}{3} cos (3 x)

= 7 x sin (3 x) + \frac{7}{3} cos (3 x) - (- \frac{8}{3} cos (3 x))

Simplify

7 x sin (3 x) + \frac{7}{3} cos (3 x) - (- \frac{8}{3} cos (3 x)) : 7 x sin (3 x) + 5 cos (3 x)

= 7 x sin (3 x) + 5 cos (3 x)

Add a constant to the solution

= 7 x sin (3 x) + 5 cos (3 x) + C

What is the integral of 21xcos(3x)-8sin(3x) ?
The integral of 21xcos(3x)-8sin(3x) is 7xsin(3x)+5cos(3x)+C