What is the integral of cos^3(x/(13)) ?

The integral of cos^3(x/(13)) is 13(sin(x/(13))-(sin^3(x/(13)))/3)+C

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integral of cos^3(x/(13))

\int cos^{3} (\frac{x}{13}) d x

13 (sin (\frac{x}{13}) - \frac{sin ^{3} ( \frac{x}{13} )}{3}) + C

Solution steps

\int cos^{3} (\frac{x}{13}) d x

Apply u-substitution

: \int cos^{3} (u) \cdot 13 d u

= \int cos^{3} (u) \cdot 13 d u

Take the constant out:

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

= 13 \cdot \int cos^{3} (u) d u

Rewrite using trig identities

= 13 \cdot \int (1 - sin^{2} (u)) cos (u) d u

Apply u-substitution

: \int 1 - v^{2} d v

= 13 \cdot \int 1 - v^{2} d v

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 13 (\int 1 d v - \int v^{2} d v)

\int 1 d v = v

\int v^{2} d v = \frac{v ^{3}}{3}

= 13 (v - \frac{v ^{3}}{3})

Substitute back

= 13 (sin (\frac{x}{13}) - \frac{sin ^{3} ( \frac{x}{13} )}{3})

Add a constant to the solution

= 13 (sin (\frac{x}{13}) - \frac{sin ^{3} ( \frac{x}{13} )}{3}) + C

x \to 0 lim (x + 6)

y = (9 x^{4} + 5 x)^{3}

\int e^{8 x + 7} d x

\frac{d x}{d t} = b (1 - x) x

\frac{\partial}{\partial x} (x (x + y)^{2})

What is the integral of cos^3(x/(13)) ?
The integral of cos^3(x/(13)) is 13(sin(x/(13))-(sin^3(x/(13)))/3)+C