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

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

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

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

2 x + tan (x) + C

Solution steps

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

\int 3 d x = 3 x

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

= 3 x - x + tan (x)

Simplify

= 2 x + tan (x)

Add a constant to the solution

= 2 x + tan (x) + C

\int \frac{x ^{4}}{7 - x ^{5}} d x

x \to 1 lim (x^{2})

\frac{\partial}{\partial x} (e^{(x + y + 1)})

\int_{a}^{b} x^{2} (\frac{1}{b - a}) d x

(x + 3)^{3 x - 2}

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