What is the integral of sec(x)tan(x)cos(sec(x)) ?

The integral of sec(x)tan(x)cos(sec(x)) is sin(sec(x))+C

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integral of sec(x)tan(x)cos(sec(x))

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

sin (sec (x)) + C

Solution steps

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

Apply u-substitution

= \int cos (u) d u

Use the common integral:

\int cos (u) d u = sin (u)

= sin (u)

Substitute back

u = sec (x)

= sin (sec (x))

Add a constant to the solution

= sin (sec (x)) + C

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What is the integral of sec(x)tan(x)cos(sec(x)) ?
The integral of sec(x)tan(x)cos(sec(x)) is sin(sec(x))+C