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

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

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integral of sec(3t)tan(3t)

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

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

Solution steps

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

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 t)

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

Add a constant to the solution

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

y^{^{''}} + 5 y^{^{'}} + 10 y = 510 e^{2 t} cos (6 t)

\int \frac{x ^{2}}{6 x - x ^{2}} d x

y^{^{'}} + x y = e^{x} y

\int \frac{8 t ^{3} + 10}{4 t ^{2} - 4 t + 5} d t

\int x^{4} + 1 d x

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