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

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

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integral of tan(t)sec(t)

\int tan (t) sec (t) d t

sec (t) + C

Solution steps

\int tan (t) sec (t) d t

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 (t)

= 1 \cdot sec (t)

Simplify

= sec (t)

Add a constant to the solution

= sec (t) + C

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