What is the integral of xtan(x)sec(x) ?

The integral of xtan(x)sec(x) is xsec(x)-ln|tan(x)+sec(x)|+C

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integral of xtan(x)sec(x)

\int x tan (x) sec (x) d x

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

Solution steps

\int x tan (x) sec (x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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What is the integral of xtan(x)sec(x) ?
The integral of xtan(x)sec(x) is xsec(x)-ln|tan(x)+sec(x)|+C