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

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

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integral of 4cos(x-1)

\int 4 cos (x - 1) d x

4 sin (x - 1) + C

Solution steps

\int 4 cos (x - 1) d x

Take the constant out:

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

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

Apply u-substitution

: \int cos (u) d u

= 4 \cdot \int cos (u) d u

Use the common integral:

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

= 4 sin (u)

Substitute back

u = x - 1

= 4 sin (x - 1)

Add a constant to the solution

= 4 sin (x - 1) + C

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