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

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

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integral of 3+3tan^2(x)

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

3 tan (x) + C

Solution steps

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

3 + 3 tan^{2} (x) = 3 (1 + tan^{2} (x))

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Rewrite using trig identities

= 3 \cdot \int sec^{2} (x) d x

Use the common integral:

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

= 3 tan (x)

Add a constant to the solution

= 3 tan (x) + C

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