What is the integral of 4cos(1-x) ?

The integral of 4cos(1-x) is -4sin(1-x)+C

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integral of 4cos(1-x)

\int 4 cos (1 - x) d x

- 4 sin (1 - x) + C

Solution steps

\int 4 cos (1 - x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int cos (1 - x) d x

Apply Integration By Parts

= 4 (cos (1 - x) x - \int sin (1 - x) x d x)

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

= 4 (cos (1 - x) x - (x cos (1 - x) + sin (1 - x)))

Simplify

4 (cos (1 - x) x - (x cos (1 - x) + sin (1 - x))) : - 4 sin (1 - x)

= - 4 sin (1 - x)

Add a constant to the solution

= - 4 sin (1 - x) + C