What is the integral of sin(-x+1) ?

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

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integral of sin(-x+1)

\int sin (- x + 1) d x

cos (- x + 1) + C

Solution steps

\int sin (- x + 1) d x

Apply u-substitution

: \int - sin (u) d u

= \int - sin (u) d u

Take the constant out:

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

= - \int sin (u) d u

Use the common integral:

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

= - (- cos (u))

Substitute back

u = - x + 1

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

Simplify

= cos (- x + 1)

Add a constant to the solution

= cos (- x + 1) + C

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