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

\frac{5 x ^{3}}{( 5 - 3 x ) ^{4}}

f (x) = 5 (x^{3} - x)^{4}

\frac{d}{d x} (\frac{( x - 2 )}{x - 1})

h (x) = (x + 1)^{7} - 7 x - 3

\int e^{x} cos (7 x) d x

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