What is the integral of (sec(2x)tan(2x)) ?

The integral of (sec(2x)tan(2x)) is 1/2 cos(2x)+1/2 sin(2x)tan(2x)+C

integral of (sec(2x)tan(2x))

\int (sec (2 x) tan (2 x)) d x

\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

Solution steps

\int sec (2 x) tan (2 x) d x

Rewrite using trig identities

= \int \frac{sin ( 2 x )}{cos ^{2} ( 2 x )} d x

Apply Integration By Parts

= - \int sin (2 x) d x + \frac{1}{2} sin (2 x) tan (2 x)

\int sin (2 x) d x = - \frac{1}{2} cos (2 x)

= - (- \frac{1}{2} cos (2 x)) + \frac{1}{2} sin (2 x) tan (2 x)

Simplify

= \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)

Add a constant to the solution

= \frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x) + C

\int \frac{m ^{3}}{( z ^{2} ) ^{3}} d m

\frac{\partial}{\partial y} (x e^{x y})

\int \frac{( ln ( x ) ) ^{3}}{3 x} d x

n = 0 \sum \infty \frac{n x ^{n}}{n + 8}

\int \frac{3 x}{2 x ^{2} + 3 x + 4} d x

What is the integral of (sec(2x)tan(2x)) ?
The integral of (sec(2x)tan(2x)) is 1/2 cos(2x)+1/2 sin(2x)tan(2x)+C