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

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

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integral of sin(-2x+1)

integral

sin (- 2 x + 1)

\frac{1}{2} cos (- 2 x + 1) + C

Solution steps

\int sin (- 2 x + 1) d x

Apply u-substitution

: \int - \frac{1}{2} sin (u) d u

= \int - \frac{1}{2} sin (u) d u

Take the constant out:

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

= - \frac{1}{2} \cdot \int sin (u) d u

Use the common integral:

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

= - \frac{1}{2} (- cos (u))

Substitute back

u = - 2 x + 1

= - \frac{1}{2} (- cos (- 2 x + 1))

Simplify

= \frac{1}{2} cos (- 2 x + 1)

Add a constant to the solution

= \frac{1}{2} cos (- 2 x + 1) + C

t^{- 4}

\frac{x ^{2}}{( x ^{2} - 3 x + 2 )}

\frac{1}{( x + 2 ) ^{2} \cdot ( \frac{1}{x} )}

(2 x)^{3}

\frac{1}{( x ^{2} + 2 x ) ^{\frac{1}{2}}}

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