What is the integral of cos(2x-3) ?

The integral of cos(2x-3) is 1/2 sin(2x-3)+C

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integral of cos(2x-3)

\int cos (2 x - 3) d x

\frac{1}{2} sin (2 x - 3) + C

Solution steps

\int cos (2 x - 3) d x

Rewrite using trig identities

= \int cos (2 x) cos (3) + sin (2 x) sin (3) 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 cos (2 x) cos (3) d x + \int sin (2 x) sin (3) d x

\int cos (2 x) cos (3) d x = cos (3) \frac{1}{2} sin (2 x)

\int sin (2 x) sin (3) d x = - \frac{1}{2} sin (3) cos (2 x)

= cos (3) \frac{1}{2} sin (2 x) - \frac{1}{2} sin (3) cos (2 x)

Use the Angle Difference identity:

sin (s) cos (t) - cos (s) sin (t) = sin (s - t)

= \frac{1}{2} sin (2 x - 3)

Add a constant to the solution

= \frac{1}{2} sin (2 x - 3) + C

What is the integral of cos(2x-3) ?
The integral of cos(2x-3) is 1/2 sin(2x-3)+C