What is the integral of tan(4x)sec(4x) ?

The integral of tan(4x)sec(4x) is 1/4 sec(4x)+C

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integral of tan(4x)sec(4x)

\int tan (4 x) sec (4 x) d x

\frac{1}{4} sec (4 x) + C

Solution steps

\int tan (4 x) sec (4 x) d x

Apply u-substitution

: \int \frac{1}{4} d u

= \int \frac{1}{4} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{4} u

Substitute back

u = sec (4 x)

= \frac{1}{4} sec (4 x)

Add a constant to the solution

= \frac{1}{4} sec (4 x) + C

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What is the integral of tan(4x)sec(4x) ?
The integral of tan(4x)sec(4x) is 1/4 sec(4x)+C