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

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

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integral of cos(1/5 x)

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

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

Solution steps

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

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} x

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

Add a constant to the solution

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

\int sin (x) + 1 d x

\frac{d}{d x} (ln (c) os x)

\frac{d x}{d t} = 6 x t^{4}

\frac{d}{d x} (x^{2} - 16 ln (x^{2}))

f (x) = 10 x - 12 + \frac{27}{x ^{4}}

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