What is the integral of (tan^2(3x))+10 ?

The integral of (tan^2(3x))+10 is 9x+1/3 tan(3x)+C

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integral of (tan^2(3x))+10

\int (tan^{2} (3 x)) + 10 d x

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

Solution steps

\int tan^{2} (3 x) + 10 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} (3 x) d x + \int 10 d x

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

\int 10 d x = 10 x

= - x + \frac{1}{3} tan (3 x) + 10 x

Simplify

= 9 x + \frac{1}{3} tan (3 x)

Add a constant to the solution

= 9 x + \frac{1}{3} tan (3 x) + C

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What is the integral of (tan^2(3x))+10 ?
The integral of (tan^2(3x))+10 is 9x+1/3 tan(3x)+C