What is the integral of ((1+cos(3t))/2) ?

The integral of ((1+cos(3t))/2) is 1/2 (t+1/3 sin(3t))+C

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integral of ((1+cos(3t))/2)

\int (\frac{1 + cos ( 3 t )}{2}) d t

\frac{1}{2} (t + \frac{1}{3} sin (3 t)) + C

Solution steps

\int \frac{1 + cos ( 3 t )}{2} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int 1 + cos (3 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

= \frac{1}{2} (\int 1 d t + \int cos (3 t) d t)

\int 1 d t = t

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

= \frac{1}{2} (t + \frac{1}{3} sin (3 t))

Add a constant to the solution

= \frac{1}{2} (t + \frac{1}{3} sin (3 t)) + C

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

\int 3 x^{2} - 18 x + 27 d x

\frac{d}{d x} (\frac{1}{x ^{7}})

\frac{4 s}{s ^{2} + 8 s + 20}

\frac{d}{d x} ((3 x^{2} - 6 x - sin (x))^{4})

What is the integral of ((1+cos(3t))/2) ?
The integral of ((1+cos(3t))/2) is 1/2 (t+1/3 sin(3t))+C