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

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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} 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

x \to 6 lim (\frac{x}{6 - x})

x \to 0 lim (x^{2 x^{2}})

ln (1 + x) 0

y = \frac{1}{1 + x ^{2}}

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