What is the integral of 1/(tan(5θ)) ?

The integral of 1/(tan(5θ)) is 1/5 ln|sin(5θ)|+C

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integral of 1/(tan(5θ))

\int \frac{1}{tan ( 5 θ )} d θ

\frac{1}{5} ln ∣ sin (5 θ) ∣ + C

Solution steps

\int \frac{1}{tan ( 5 θ )} d θ

Rewrite using trig identities

= \int \frac{cos ( 5 θ )}{sin ( 5 θ )} d θ

Apply u-substitution

: \int \frac{1}{5 u} d u

= \int \frac{1}{5 u} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{5} ln ∣ u ∣

Substitute back

u = sin (5 θ)

= \frac{1}{5} ln ∣ sin (5 θ) ∣

Add a constant to the solution

= \frac{1}{5} ln ∣ sin (5 θ) ∣ + C

f (x) = x^{\frac{1}{2}}

\int_{1}^{2} ln (x - 1) d x

f (x) = e^{x} - x

\int \frac{cos ( \frac{x}{3} )}{sin ^{4} ( \frac{x}{3} )} d x

\int e^{7 x} cos (3 x) d x

What is the integral of 1/(tan(5θ)) ?
The integral of 1/(tan(5θ)) is 1/5 ln|sin(5θ)|+C