What is the integral of cos(x/9) ?

The integral of cos(x/9) is 9sin(x/9)+C

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integral of cos(x/9)

\int cos (\frac{x}{9}) d x

9 sin (\frac{x}{9}) + C

Solution steps

\int cos (\frac{x}{9}) d x

Apply u-substitution

: \int cos (u) \cdot 9 d u

= \int cos (u) \cdot 9 d u

Take the constant out:

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

= 9 \cdot \int cos (u) d u

Use the common integral:

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

= 9 sin (u)

Substitute back

u = \frac{x}{9}

= 9 sin (\frac{x}{9})

Add a constant to the solution

= 9 sin (\frac{x}{9}) + C

(3, - 29), (- 1, 7)

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{- 3 t}

\int_{1}^{5} \frac{ln ( x )}{x} d x

\int_{- \infty}^{0} \frac{1}{5 - 9 x} d x

3 e^{4 t}