What is the integral of (sin(x))^{-1} ?

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

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integral of (sin(x))^{-1}

\int (sin (x))^{- 1} d x

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

Solution steps

\int (sin (x))^{- 1} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

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

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

Add a constant to the solution

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

- x, x - x^{2}, 0, 2

\int \frac{x ^{3}}{1} + x^{4} d x

\int cos (n \cdot x) d x

n = 1 \sum \infty \frac{1}{( 2 n + 1 ) ^{3}}

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