What is the integral of cot(x/7) ?

The integral of cot(x/7) is 7ln|sin(x/7)|+C

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integral of cot(x/7)

\int cot (\frac{x}{7}) d x

7 ln sin (\frac{x}{7}) + C

Solution steps

\int cot (\frac{x}{7}) d x

Rewrite using trig identities

= \int \frac{cos ( \frac{x}{7} )}{sin ( \frac{x}{7} )} d x

Apply u-substitution

: \int \frac{7}{u} d u

= \int \frac{7}{u} d u

Take the constant out:

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

= 7 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 7 ln ∣ u ∣

Substitute back

u = sin (\frac{x}{7})

= 7 ln sin (\frac{x}{7})

Add a constant to the solution

= 7 ln sin (\frac{x}{7}) + C

\frac{d}{d x} (2 x - 4)

2^{2^{n}}

\int \frac{1}{x ^{2} a ^{2} + x ^{2}} d x

e^{- t}

\frac{d}{d x} (c x^{- 4})