What is the integral of 2/(sin(x)) ?

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

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integral of 2/(sin(x))

\int \frac{2}{sin ( x )} d x

2 ln tan (\frac{x}{2}) + C

Solution steps

\int \frac{2}{sin ( x )} d x

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = tan (\frac{x}{2})

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

Add a constant to the solution

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

\frac{\partial}{\partial x} (x^{0.25} y^{0.75})

y^{^{'}} + sin (t) y = sin (t), y (0) = 3

\int (- 2 y) d y

\frac{d y}{d x} = \frac{4}{x ^{2} e ^{3 y + 9}}

\frac{\partial}{\partial x} (x^{4} y^{3})

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