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

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

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integral of sec(4θ)tan(4θ)

\int sec (4 θ) tan (4 θ) d θ

\frac{1}{4} sec (4 θ) + C

Solution steps

\int sec (4 θ) tan (4 θ) d θ

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 θ)

= \frac{1}{4} sec (4 θ)

Add a constant to the solution

= \frac{1}{4} sec (4 θ) + C

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