What is the integral of cot(7x) ?

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

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

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

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

\frac{d}{d x} (csc^{7} (x))

\int \frac{x + 2}{( x ^{2} + 2 x + 10 ) ^{\frac{5}{2}}} d x

0 = 2 x + 1 - 2 y y^{^{'}}, y (- 2) = - 1