What is the integral of 2(1+tan^2(a)) ?

The integral of 2(1+tan^2(a)) is 2tan(a)+C

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integral of 2(1+tan^2(a))

\int 2 (1 + tan^{2} (a)) d a

2 tan (a) + C

Solution steps

\int 2 (1 + tan^{2} (a)) d a

Take the constant out:

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

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

Rewrite using trig identities

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

Use the common integral:

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

= 2 tan (a)

Add a constant to the solution

= 2 tan (a) + C

x \to 0 lim (sec^{2} (x))

\frac{d}{d x} (380000 x - \frac{1}{32} x^{2})

\int (4 x - 8 y^{3}) d y

\int - \frac{1}{4} cos (2 x) d x

y^{^{''}} - 2 y^{^{'}} + y = 24 x^{2} e^{x}

What is the integral of 2(1+tan^2(a)) ?
The integral of 2(1+tan^2(a)) is 2tan(a)+C