What is the integral of 1/(2tan(x)) ?

The integral of 1/(2tan(x)) is 1/2 ln|sin(x)|+C

Popular >

integral of 1/(2tan(x))

\int \frac{1}{2 tan ( x )} d x

\frac{1}{2} ln ∣ sin (x) ∣ + C

Solution steps

\int \frac{1}{2 tan ( x )} d x

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{tan ( x )} d x

Rewrite using trig identities

= \frac{1}{2} \cdot \int \frac{cos ( x )}{sin ( x )} d x

Apply u-substitution

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

= \frac{1}{2} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = sin (x)

= \frac{1}{2} ln ∣ sin (x) ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ sin (x) ∣ + C

\int (\frac{2 x}{x ^{2} + 1} + sec^{2} (x)) d x

\int \frac{4 x - 5}{2 x ^{3} - 5 x ^{2} - 3 x} d x

\int (3 x^{2} + 5 x - 4) d x

\int \frac{11}{3 - 2 x} d x

\int 3 + e^{x} d x

What is the integral of 1/(2tan(x)) ?
The integral of 1/(2tan(x)) is 1/2 ln|sin(x)|+C