What is the integral of cot(7x) ?

The integral of cot(7x) is 1/7 ln|sin(7x)|+C

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integral of cot(7x)

\int cot (7 x) d x

\frac{1}{7} ln ∣ sin (7 x) ∣ + C

Solution steps

\int cot (7 x) d x

Rewrite using trig identities

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

Apply u-substitution

: \int \frac{1}{7 u} d u

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

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{7} ln ∣ u ∣

Substitute back

u = sin (7 x)

= \frac{1}{7} ln ∣ sin (7 x) ∣

Add a constant to the solution

= \frac{1}{7} ln ∣ sin (7 x) ∣ + C

\frac{d}{d x} (\frac{3 - 4 x}{2 x + 2})

\int sin (x) \cdot (π + 2 x) d x

\frac{d y}{d x} = \frac{( y ^{2} + 5 x x ^{2} + y ^{2} )}{x y}

\frac{d}{d t} ((4 cos (t) - 2) e^{i t})

\frac{d}{d x} ((ln (4 x))^{2})