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

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

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integral of sin(x)+3cos(x)

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

- cos (x) + 3 sin (x) + C

Solution steps

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

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

\int 3 cos (x) d x = 3 sin (x)

= - cos (x) + 3 sin (x)

Add a constant to the solution

= - cos (x) + 3 sin (x) + C

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

x \to 4 - lim (\frac{3}{x ^{2} - 16})

y = tan (2) (x)

3 arcsin (x^{4})

\frac{d}{d x} (- 131072 sin (2 x))

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