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

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

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integral of (1-cos(x))

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

x - sin (x) + C

Solution steps

\int 1 - cos (x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

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

\int 1 d x = x

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

= x - sin (x)

Add a constant to the solution

= x - sin (x) + C

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

\int (4 - x) x d x

y^{^{'}} + 3 y = t + e^{(- 2 t)}

x \to - 3 lim (\frac{1}{( x + 3 ) ^{2}})

y^{^{'}} - e^{x} e^{y} = - 1