What is the integral of sin(x-4) ?

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

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integral of sin(x-4)

\int sin (x - 4) d x

x sin (x - 4) + x sin (4 - x) - cos (4 - x) + C

Solution steps

\int sin (x - 4) d x

Apply Integration By Parts

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

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

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

Simplify

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

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

Add a constant to the solution

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

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What is the integral of sin(x-4) ?
The integral of sin(x-4) is xsin(x-4)+xsin(4-x)-cos(4-x)+C