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

The integral of sin(3t)+cos(t) is -1/3 cos(3t)+sin(t)+C

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

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

- \frac{1}{3} cos (3 t) + sin (t) + C

Solution steps

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

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 (3 t) d t + \int cos (t) d t

\int sin (3 t) d t = - \frac{1}{3} cos (3 t)

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

= - \frac{1}{3} cos (3 t) + sin (t)

Add a constant to the solution

= - \frac{1}{3} cos (3 t) + sin (t) + C

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

x^{2} + y^{2} + 2 x y y^{^{'}} = 0

\int (x + 1) e^{- 2 x} d x

f (x) = \frac{x ^{2} - 2 x - 3}{x}

\frac{\partial}{\partial x} (3 x^{2} - 12 y)

What is the integral of sin(3t)+cos(t) ?
The integral of sin(3t)+cos(t) is -1/3 cos(3t)+sin(t)+C