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Popular >

integral of csc(u)

Solution

\int csc (u) d u

Solution

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

Solution steps

\int csc (u) d u

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{v} d v = ln (∣ v ∣)

= ln ∣ v ∣

Substitute back

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

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

Add a constant to the solution

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

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Frequently Asked Questions (FAQ)

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