What is the integral of sin(x-3) ?

The integral of sin(x-3) is xsin(x-3)+xsin(3-x)-cos(3-x)+C

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integral of sin(x-3)

\int sin (x - 3) d x

x sin (x - 3) + x sin (3 - x) - cos (3 - x) + C

Solution steps

\int sin (x - 3) d x

Apply Integration By Parts

: sin (x - 3) x - \int cos (x - 3) x d x

= sin (x - 3) x - \int cos (x - 3) x d x

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

= sin (x - 3) x - (- x sin (3 - x) + cos (3 - x))

Simplify

sin (x - 3) x - (- x sin (3 - x) + cos (3 - x)) : x sin (x - 3) + x sin (3 - x) - cos (3 - x)

= x sin (x - 3) + x sin (3 - x) - cos (3 - x)

Add a constant to the solution

= x sin (x - 3) + x sin (3 - x) - cos (3 - x) + C

3 cos (x) + 2 sin (x)

\int \frac{1}{e ^{2 x} + e ^{x}} d x

(\frac{x}{3})^{^{'}}

y - x \frac{d y}{d x} = 0

y^{^{'}} = \frac{y}{1 + x ^{2}}

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