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

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

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

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

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

Solution steps

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

Apply Integral Substitution

= \int \frac{1}{a ( 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}{a} \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}{a} arctan (u)

Substitute back

u = \frac{x}{a}

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

Add a constant to the solution

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

y^{^{'}} = \frac{( 1 - x - y )}{x + y}

\frac{1}{4} q^{^{''}} + 20 q^{^{'}} + 300 q = 0

\int 2^{X} d X

\frac{2}{x + 1}

\frac{\partial}{\partial x} ((x + 2 y^{3})^{\frac{1}{3}})

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