What is the integral of 20cos(10t+pi/6) ?

The integral of 20cos(10t+pi/6) is 2sin(10t+pi/6)+C

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integral of 20cos(10t+pi/6)

\int 20 cos (10 t + \frac{π}{6}) d t

2 sin (10 t + \frac{π}{6}) + C

Solution steps

\int 20 cos (10 t + \frac{π}{6}) d t

Take the constant out:

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

= 20 \cdot \int cos (10 t + \frac{π}{6}) d t

Apply u-substitution

= 20 \cdot \int cos (u) \frac{1}{10} d u

Take the constant out:

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

= 20 \cdot \frac{1}{10} \cdot \int cos (u) d u

Use the common integral:

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

= 20 \cdot \frac{1}{10} sin (u)

Substitute back

u = 10 t + \frac{π}{6}

= 20 \cdot \frac{1}{10} sin (10 t + \frac{π}{6})

Simplify

20 \cdot \frac{1}{10} sin (10 t + \frac{π}{6}) : 2 sin (10 t + \frac{π}{6})

= 2 sin (10 t + \frac{π}{6})

Add a constant to the solution

= 2 sin (10 t + \frac{π}{6}) + C

What is the integral of 20cos(10t+pi/6) ?
The integral of 20cos(10t+pi/6) is 2sin(10t+pi/6)+C