What is the integral of csc(x+1) ?

The integral of csc(x+1) is ln|tan((x+1)/2)|+C

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integral of csc(x+1)

\int csc (x + 1) d x

ln tan (\frac{x + 1}{2}) + C

Solution steps

\int csc (x + 1) d x

Apply u-substitution

: \int csc (u) d u

= \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

= ln tan (\frac{x + 1}{2})

Add a constant to the solution

= ln tan (\frac{x + 1}{2}) + C

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What is the integral of csc(x+1) ?
The integral of csc(x+1) is ln|tan((x+1)/2)|+C