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

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

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

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

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

Solution steps

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

\frac{d}{d x} ((\frac{4}{5} x)^{5})

y = sin (x), y = cos (x), x = 0, x = 2 π

\frac{d}{d x} (e^{x^{6}} + lo g_{5} (π))

\frac{\partial}{\partial x} (2 x + 3 y - 6)

(9 - x^{3})^{- 2}

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