What is the integral of tsec^2(t) ?

The integral of tsec^2(t) is ttan(t)+ln|cos(t)|+C

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integral of tsec^2(t)

\int t sec^{2} (t) d t

t tan (t) + ln ∣ cos (t) ∣ + C

Solution steps

\int t sec^{2} (t) d t

Apply Integration By Parts

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

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

\int tan (t) d t = - ln ∣ cos (t) ∣

= t tan (t) - (- ln ∣ cos (t) ∣)

Simplify

= t tan (t) + ln ∣ cos (t) ∣

Add a constant to the solution

= t tan (t) + ln ∣ cos (t) ∣ + C

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What is the integral of tsec^2(t) ?
The integral of tsec^2(t) is ttan(t)+ln|cos(t)|+C