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

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

integral of sec(2t)tan(2t)

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

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

Solution steps

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

Rewrite using trig identities

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

Apply Integration By Parts

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

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

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

Simplify

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

Add a constant to the solution

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

d er i v a t i v e (8 x - 6)^{2}

\int (\frac{x ^{2} + 5}{( x + 2 ) ^{2}}) d x

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

l a pl a ce t r an s f or m sin (2 x + 3)

x \to 0 lim (x^{3} cos (\frac{5}{x}))

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