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 y}{d x} = 4 y e^{x + 4}

(x + y) d y = (x - y) d x

f (x) = x^{4} - 13 x^{2} + 36, at x = - 2

\frac{d}{d x} (5 x^{3} - 5 x)

\frac{\partial}{\partial x} (cos (0.6 x - t))

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