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

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

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integral of tan(3x)sec(3x)

\int tan (3 x) sec (3 x) d x

\frac{1}{3} sec (3 x) + C

Solution steps

\int tan (3 x) sec (3 x) d x

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 x)

= \frac{1}{3} sec (3 x)

Add a constant to the solution

= \frac{1}{3} sec (3 x) + C

\int \frac{1}{( x ^{2} - 4 x )} d x

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\int t (1 - t^{2})^{10} d t

\int \frac{sec ^{2} ( x )}{2} d x

\int \frac{2}{2 + x} d x

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