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

\frac{d}{d x} (arcsin (\frac{x}{8}))

\frac{d y}{d x} + 5 y = 3 sin (e^{5 x})

\frac{1}{5 x}

\int \frac{1}{6 x ^{3} - 7 x ^{2} - 3 x} d x

\frac{\partial}{\partial v} (sin (u) cos (v))