What is the integral of tan^2(2x)+4 ?

The integral of tan^2(2x)+4 is 3x+1/2 tan(2x)+C

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integral of tan^2(2x)+4

\int tan^{2} (2 x) + 4 d x

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

Solution steps

\int tan^{2} (2 x) + 4 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 tan^{2} (2 x) d x + \int 4 d x

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

\int 4 d x = 4 x

= - x + \frac{1}{2} tan (2 x) + 4 x

Simplify

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

Add a constant to the solution

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

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What is the integral of tan^2(2x)+4 ?
The integral of tan^2(2x)+4 is 3x+1/2 tan(2x)+C