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

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

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

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

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

Solution steps

\int sec (3 x) tan (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{3}{x} - \frac{10}{x ^{6}}) d x

\frac{d}{d x} (\frac{1}{( 2 x + 1 ) ^{3}})

\int 1 + t d t

\frac{d}{d x} (\frac{( x + 30 ) x ^{2} + 100}{x})

f (x) = 9 + 4 x

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