What is the integral of 1/(sin(y/2)) ?

The integral of 1/(sin(y/2)) is 2ln|tan(y/4)|+C

Popular >

integral of 1/(sin(y/2))

\int \frac{1}{sin ( \frac{y}{2} )} d y

2 ln tan (\frac{y}{4}) + C

Solution steps

\int \frac{1}{sin ( \frac{y}{2} )} d y

Apply u-substitution

: \int 2 csc (u) d u

= \int 2 csc (u) d u

Take the constant out:

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

= 2 \cdot \int csc (u) d u

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= 2 ln ∣ v ∣

Substitute back

= 2 ln tan (\frac{\frac{y}{2}}{2})

\frac{\frac{y}{2}}{2} = \frac{y}{4}

= 2 ln tan (\frac{y}{4})

Add a constant to the solution

= 2 ln tan (\frac{y}{4}) + C

\int_{0}^{t} \frac{1}{1 + r} d r

\int - 4 x - 8 d x

n = 1 \sum \infty 5 e^{- 6 n}

\int_{0}^{1} 3 (1 + x)^{8} d x

\int csc^{4} (5 x) cot^{4} (5 x) d x

What is the integral of 1/(sin(y/2)) ?
The integral of 1/(sin(y/2)) is 2ln|tan(y/4)|+C