What is the integral of cotan^2(x/4) ?

The integral of cotan^2(x/4) is co(-x+4tan(x/4))+C

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integral of cotan^2(x/4)

\int co tan^{2} (\frac{x}{4}) d x

co (- x + 4 tan (\frac{x}{4})) + C

Solution steps

\int co tan^{2} (\frac{x}{4}) d x

Take the constant out:

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

= co \cdot \int tan^{2} (\frac{x}{4}) d x

Rewrite using trig identities

= co \cdot \int - 1 + sec^{2} (\frac{x}{4}) 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

= co (- \int 1 d x + \int sec^{2} (\frac{x}{4}) d x)

\int 1 d x = x

\int sec^{2} (\frac{x}{4}) d x = 4 tan (\frac{x}{4})

= co (- x + 4 tan (\frac{x}{4}))

Add a constant to the solution

= co (- x + 4 tan (\frac{x}{4})) + C

What is the integral of cotan^2(x/4) ?
The integral of cotan^2(x/4) is co(-x+4tan(x/4))+C