What is the integral of 2sin(x-1) ?

The integral of 2sin(x-1) is 2(xsin(x-1)+xsin(1-x)-cos(1-x))+C

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integral of 2sin(x-1)

\int 2 sin (x - 1) d x

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

Solution steps

\int 2 sin (x - 1) d x

Take the constant out:

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

= 2 \cdot \int sin (x - 1) d x

Apply Integration By Parts

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

= 2 (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)

= 2 (sin (x - 1) x - (- x sin (1 - x) + cos (1 - x)))

Expand

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

= 2 (x sin (x - 1) + x sin (1 - x) - cos (1 - x))

Add a constant to the solution

= 2 (x sin (x - 1) + x sin (1 - x) - cos (1 - x)) + C

\frac{d x}{d t} = sin (π x)

\frac{d}{d x} (ln (x^{2} + y^{2} + 1))

x \to \infty + lim (\frac{( 5 x ^{3} + 7 x ^{2} - 8 x + 9 )}{11 x ^{2} + 7 x - 6})

\int sin^{4} (7 x) d x

\frac{1}{( s - 5 ) ^{2}}

What is the integral of 2sin(x-1) ?
The integral of 2sin(x-1) is 2(xsin(x-1)+xsin(1-x)-cos(1-x))+C