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

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

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

\int sec^{2} (x) + sec (2 x) tan (2 x) d x

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

Solution steps

\int sec^{2} (x) + sec (2 x) tan (2 x) d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int sec^{2} (x) d x + \int sec (2 x) tan (2 x) d x

\int sec^{2} (x) d x = tan (x)

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

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

Add a constant to the solution

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

p (θ) = 7 θ

f (x) = ln (x + 4)

\int \frac{1}{2 sin ( x ) - 3 cos ( x ) - 5} d x

x \to \infty lim (\frac{0}{0})

\frac{s + 3}{( s + 1 ) ^{2}}

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