What is the integral of x*(sec(x))^2 ?

The integral of x*(sec(x))^2 is xtan(x)+ln|cos(x)|+C

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integral of x*(sec(x))^2

\int x \cdot (sec (x))^{2} d x

x tan (x) + ln ∣ cos (x) ∣ + C

Solution steps

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

Simplify

= \int x sec^{2} (x) d x

Apply Integration By Parts

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

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

\int tan (x) d x = - ln ∣ cos (x) ∣

= x tan (x) - (- ln ∣ cos (x) ∣)

Simplify

= x tan (x) + ln ∣ cos (x) ∣

Add a constant to the solution

= x tan (x) + ln ∣ cos (x) ∣ + C

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What is the integral of x*(sec(x))^2 ?
The integral of x*(sec(x))^2 is xtan(x)+ln|cos(x)|+C