What is the integral of (csc(x)) ?

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

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integral of (csc(x))

\int (csc (x)) d x

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

Solution steps

\int csc (x) 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

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