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

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

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integral of cos(1-x)

\int cos (1 - x) d x

- sin (1 - x) + C

Solution steps

\int cos (1 - x) d x

Apply Integration By Parts

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

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

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

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

Simplify

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

= - sin (1 - x)

Add a constant to the solution

= - sin (1 - x) + C

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

y = 4 x - 1, (1, - 4)

\frac{\partial}{\partial x} (4 x sin (x y))

\frac{d}{d x} (e^{x} cos (8 x))

f (x) = \frac{x}{x - 3}, at x = 1