What is the integral of (sin(x)+3) ?

The integral of (sin(x)+3) is -cos(x)+3x+C

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integral of (sin(x)+3)

\int (sin (x) + 3) d x

- cos (x) + 3 x + C

Solution steps

\int sin (x) + 3 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 sin (x) d x + \int 3 d x

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

\int 3 d x = 3 x

= - cos (x) + 3 x

Add a constant to the solution

= - cos (x) + 3 x + C

\int e^{6}

y = cos (4 x)

\int \frac{1 - 2 x}{x ^{2}} d x

\frac{d}{d x} (ln (3 x - 2))