What is the integral of (1/(x^2+4)) ?

The integral of (1/(x^2+4)) is 1/2 arctan(x/2)+C

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integral of (1/(x^2+4))

\int (\frac{1}{x ^{2} + 4}) d x

\frac{1}{2} arctan (\frac{x}{2}) + C

Solution steps

\int \frac{1}{x ^{2} + 4} d x

Apply Integral Substitution

= \int \frac{1}{2 ( u ^{2} + 1 )} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= \frac{1}{2} arctan (u)

Substitute back

u = \frac{x}{2}

= \frac{1}{2} arctan (\frac{x}{2})

Add a constant to the solution

= \frac{1}{2} arctan (\frac{x}{2}) + C

x \to 0 - lim (\frac{e ^{x} - 1}{e ^{x}})

\frac{d}{d x} (\frac{x ^{2} + 4}{x})

\frac{1}{2 s + 3}

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

x \to \infty lim (\frac{sin ( 13 x )}{3 x})

What is the integral of (1/(x^2+4)) ?
The integral of (1/(x^2+4)) is 1/2 arctan(x/2)+C