What is the integral of 5cos(x/5) ?

The integral of 5cos(x/5) is 25sin(x/5)+C

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integral of 5cos(x/5)

\int 5 cos (\frac{x}{5}) d x

25 sin (\frac{x}{5}) + C

Solution steps

\int 5 cos (\frac{x}{5}) d x

Take the constant out:

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

= 5 \cdot \int cos (\frac{x}{5}) d x

Apply u-substitution

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

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

Use the common integral:

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

= 5 \cdot 5 sin (u)

Substitute back

u = \frac{x}{5}

= 5 \cdot 5 sin (\frac{x}{5})

Simplify

= 25 sin (\frac{x}{5})

Add a constant to the solution

= 25 sin (\frac{x}{5}) + C

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