What is the integral of sec(3θ)tan(3θ) ?

The integral of sec(3θ)tan(3θ) is 1/3 sec(3θ)+C

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integral of sec(3θ)tan(3θ)

\int sec (3 θ) tan (3 θ) d θ

\frac{1}{3} sec (3 θ) + C

Solution steps

\int sec (3 θ) tan (3 θ) d θ

Apply u-substitution

: \int \frac{1}{3} d u

= \int \frac{1}{3} d u

Integral of a constant:

\int a d x = a x

= \frac{1}{3} u

Substitute back

u = sec (3 θ)

= \frac{1}{3} sec (3 θ)

Add a constant to the solution

= \frac{1}{3} sec (3 θ) + C

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What is the integral of sec(3θ)tan(3θ) ?
The integral of sec(3θ)tan(3θ) is 1/3 sec(3θ)+C