What is the integral of 6sec(2x)tan(2x) ?

The integral of 6sec(2x)tan(2x) is 6(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C

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integral of 6sec(2x)tan(2x)

\int 6 sec (2 x) tan (2 x) d x

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

Solution steps

\int 6 sec (2 x) tan (2 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 6 \cdot \int sec (2 x) tan (2 x) d x

Rewrite using trig identities

= 6 \cdot \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)

= 6 (- \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)

= 6 (- (- \frac{1}{2} cos (2 x)) + \frac{1}{2} sin (2 x) tan (2 x))

Simplify

= 6 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x))

Add a constant to the solution

= 6 (\frac{1}{2} cos (2 x) + \frac{1}{2} sin (2 x) tan (2 x)) + C

\int \frac{7 x ^{3} + 6 x}{x - 1} d x

3 x^{- 2 x}

\frac{\partial}{\partial x} (\frac{m c T}{m T})

t \to 0 lim (\frac{1}{t} - \frac{1}{e ^{t} - 1})

\frac{d}{d x} (72 x)

What is the integral of 6sec(2x)tan(2x) ?
The integral of 6sec(2x)tan(2x) is 6(1/2 cos(2x)+1/2 sin(2x)tan(2x))+C