What is the integral of (ax+2)cos(x) ?

The integral of (ax+2)cos(x) is a(xsin(x)+cos(x))+2sin(x)+C

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integral of (ax+2)cos(x)

\int (a x + 2) cos (x) d x

a (x sin (x) + cos (x)) + 2 sin (x) + C

Solution steps

\int (a x + 2) cos (x) d x

Expand

(a x + 2) cos (x) : a x cos (x) + 2 cos (x)

= \int a x cos (x) + 2 cos (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 a x cos (x) d x + \int 2 cos (x) d x

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

\int 2 cos (x) d x = 2 sin (x)

= a (x sin (x) + cos (x)) + 2 sin (x)

Add a constant to the solution

= a (x sin (x) + cos (x)) + 2 sin (x) + C

What is the integral of (ax+2)cos(x) ?
The integral of (ax+2)cos(x) is a(xsin(x)+cos(x))+2sin(x)+C