What is the integral of (3+3tan^2(2x)) ?

The integral of (3+3tan^2(2x)) is 3/2 tan(2x)+C

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integral of (3+3tan^2(2x))

\int (3 + 3 tan^{2} (2 x)) d x

\frac{3}{2} tan (2 x) + C

Solution steps

\int 3 + 3 tan^{2} (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 3 d x + \int 3 tan^{2} (2 x) d x

\int 3 d x = 3 x

\int 3 tan^{2} (2 x) d x = 3 (- x + \frac{1}{2} tan (2 x))

= 3 x + 3 (- x + \frac{1}{2} tan (2 x))

Simplify

3 x + 3 (- x + \frac{1}{2} tan (2 x)) : \frac{3}{2} tan (2 x)

= \frac{3}{2} tan (2 x)

Add a constant to the solution

= \frac{3}{2} tan (2 x) + C

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What is the integral of (3+3tan^2(2x)) ?
The integral of (3+3tan^2(2x)) is 3/2 tan(2x)+C