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

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

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

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

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

Solution steps

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

\int 9 - 4 x d x

arctan (cos (x))

\int \frac{2 x ^{2} - 24}{x ( x + 2 ) ^{3}} d x

\int \frac{( x - 2 ) ^{n}}{n} d x

\frac{d}{d x} (\frac{x}{2 x - 7})

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