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

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

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integral of sec(θ)tan(θ)cos(sec(θ))

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

sin (sec (θ)) + C

Solution steps

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

Apply u-substitution

: \int cos (u) d u

= \int cos (u) d u

Use the common integral:

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

= sin (u)

Substitute back

u = sec (θ)

= sin (sec (θ))

Add a constant to the solution

= sin (sec (θ)) + C

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