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Popular >

integral of csc(t)

Solution

\int csc (t) d t

Solution

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

Solution steps

\int csc (t) d t

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{t}{2})

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

Add a constant to the solution

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

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\frac{d}{d x} (\frac{8 x ^{2} + 2 x + 8}{x})

Frequently Asked Questions (FAQ)

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