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

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

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integral of (tan(θ)sec(θ))

\int (tan (θ) sec (θ)) d θ

sec (θ) + C

Solution steps

\int tan (θ) sec (θ) d θ

Apply u-substitution

: \int 1 d u

= \int 1 d u

Integral of a constant:

\int a d x = a x

= 1 \cdot u

Substitute back

u = sec (θ)

= 1 \cdot sec (θ)

Simplify

= sec (θ)

Add a constant to the solution

= sec (θ) + C

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\frac{d}{d x} (\frac{4 csc ( x )}{5 ^{x}})

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