What is the integral of tsec(t)tan(t) ?

The integral of tsec(t)tan(t) is tsec(t)-ln|tan(t)+sec(t)|+C

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integral of tsec(t)tan(t)

\int t sec (t) tan (t) d t

t sec (t) - ln ∣ tan (t) + sec (t) ∣ + C

Solution steps

\int t sec (t) tan (t) d t

Apply Integration By Parts

: t sec (t) - \int sec (t) d t

= t sec (t) - \int sec (t) d t

\int sec (t) d t = ln ∣ tan (t) + sec (t) ∣

= t sec (t) - ln ∣ tan (t) + sec (t) ∣

Add a constant to the solution

= t sec (t) - ln ∣ tan (t) + sec (t) ∣ + C

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What is the integral of tsec(t)tan(t) ?
The integral of tsec(t)tan(t) is tsec(t)-ln|tan(t)+sec(t)|+C