What is the integral of (4+4tan^2(v)) ?

The integral of (4+4tan^2(v)) is 4tan(v)+C

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integral of (4+4tan^2(v))

\int (4 + 4 tan^{2} (v)) d v

4 tan (v) + C

Solution steps

\int 4 + 4 tan^{2} (v) d v

4 + 4 tan^{2} (v) = 4 (1 + tan^{2} (v))

= \int 4 (1 + tan^{2} (v)) d v

Take the constant out:

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

= 4 \cdot \int 1 + tan^{2} (v) d v

Rewrite using trig identities

= 4 \cdot \int sec^{2} (v) d v

Use the common integral:

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

= 4 tan (v)

Add a constant to the solution

= 4 tan (v) + C

(sin (\frac{x}{2}))^{^{'}}

\frac{\partial}{\partial x} (x y^{2} + y e^{x^{2}} + 5)

\frac{d y}{d x} + 2 x y = 2 x^{3}, y (0) = 2

\int 1 d ln (x) d x

\frac{d y}{d x} + y = x y^{2}

What is the integral of (4+4tan^2(v)) ?
The integral of (4+4tan^2(v)) is 4tan(v)+C