What is the integral of 5/6 csc^2(x/6) ?

The integral of 5/6 csc^2(x/6) is -5cot(x/6)+C

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integral of 5/6 csc^2(x/6)

\int \frac{5}{6} csc^{2} (\frac{x}{6}) d x

- 5 cot (\frac{x}{6}) + C

Solution steps

\int \frac{5}{6} csc^{2} (\frac{x}{6}) d x

Take the constant out:

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

= \frac{5}{6} \cdot \int csc^{2} (\frac{x}{6}) d x

Rewrite using trig identities

= \frac{5}{6} \cdot \int 1 + cot^{2} (\frac{x}{6}) d x

Apply the Sum Rule:

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

= \frac{5}{6} (\int 1 d x + \int cot^{2} (\frac{x}{6}) d x)

\int 1 d x = x

\int cot^{2} (\frac{x}{6}) d x = - x - 6 cot (\frac{x}{6})

= \frac{5}{6} (x - x - 6 cot (\frac{x}{6}))

Simplify

\frac{5}{6} (x - x - 6 cot (\frac{x}{6})) : - 5 cot (\frac{x}{6})

= - 5 cot (\frac{x}{6})

Add a constant to the solution

= - 5 cot (\frac{x}{6}) + C

\int \frac{( 2 x + 3 )}{x + 2} d x

f (x) = \frac{2}{3 x + 1}

5 sin (t)

\int_{0}^{1} \frac{1}{e ^{x} + 1} d x

a y^{^{'}} = b x - b y

What is the integral of 5/6 csc^2(x/6) ?
The integral of 5/6 csc^2(x/6) is -5cot(x/6)+C