What is the integral of tan(5x)sec(5x) ?

The integral of tan(5x)sec(5x) is 1/5 sec(5x)+C

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integral of tan(5x)sec(5x)

\int tan (5 x) sec (5 x) d x

\frac{1}{5} sec (5 x) + C

Solution steps

\int tan (5 x) sec (5 x) d x

Apply u-substitution

: \int \frac{1}{5} d u

= \int \frac{1}{5} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{5} u

Substitute back

u = sec (5 x)

= \frac{1}{5} sec (5 x)

Add a constant to the solution

= \frac{1}{5} sec (5 x) + C

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What is the integral of tan(5x)sec(5x) ?
The integral of tan(5x)sec(5x) is 1/5 sec(5x)+C