What is the integral of 1/2 xsec(x)tan(x) ?

The integral of 1/2 xsec(x)tan(x) is 1/2 (xsec(x)-ln|tan(x)+sec(x)|)+C

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integral of 1/2 xsec(x)tan(x)

\int \frac{1}{2} x sec (x) tan (x) d x

\frac{1}{2} (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

Solution steps

\int \frac{1}{2} x sec (x) tan (x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{2} \cdot \int x sec (x) tan (x) d x

Apply Integration By Parts

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

= \frac{1}{2} (x sec (x) - \int sec (x) d x)

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

= \frac{1}{2} (x sec (x) - ln ∣ tan (x) + sec (x) ∣)

Add a constant to the solution

= \frac{1}{2} (x sec (x) - ln ∣ tan (x) + sec (x) ∣) + C

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What is the integral of 1/2 xsec(x)tan(x) ?
The integral of 1/2 xsec(x)tan(x) is 1/2 (xsec(x)-ln|tan(x)+sec(x)|)+C