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

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

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integral of sin(x-1)

\int sin (x - 1) d x

x sin (x - 1) + x sin (1 - x) - cos (1 - x) + C

Solution steps

\int sin (x - 1) d x

Apply Integration By Parts

: sin (x - 1) x - \int cos (x - 1) x d x

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

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

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

Simplify

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

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

Add a constant to the solution

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

x = 2 y^{2}, x = 4 - y^{2}

\frac{\partial}{\partial x} (\frac{z}{x})

\int \frac{( x ^{3} + 10 )}{x ^{3} - 2 x ^{2} + 5 x} d x

\int - cos (y) d y

n = 0 \sum \infty 4 \cdot (- \frac{1}{8})^{n}

What is the integral of sin(x-1) ?
The integral of sin(x-1) is xsin(x-1)+xsin(1-x)-cos(1-x)+C