What is the integral of cos(1/5 t) ?

The integral of cos(1/5 t) is 5sin(1/5 t)+C

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integral of cos(1/5 t)

\int cos (\frac{1}{5} t) d t

5 sin (\frac{1}{5} t) + C

Solution steps

\int cos (\frac{1}{5} t) d t

Apply u-substitution

: \int cos (u) \cdot 5 d u

= \int cos (u) \cdot 5 d u

Take the constant out:

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

= 5 \cdot \int cos (u) d u

Use the common integral:

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

= 5 sin (u)

Substitute back

u = \frac{1}{5} t

= 5 sin (\frac{1}{5} t)

Add a constant to the solution

= 5 sin (\frac{1}{5} t) + C

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What is the integral of cos(1/5 t) ?
The integral of cos(1/5 t) is 5sin(1/5 t)+C