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

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

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

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

sec (x) + C

Solution steps

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

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 (x)

= 1 \cdot sec (x)

Simplify

= sec (x)

Add a constant to the solution

= sec (x) + C

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