integrate 1/(x^2+1)

1) Let's find the domain of

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

⇥ For the expression

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

to be defined, we must have:

x^{2} + 1 \neq 0

⇥The condition

x^{2} + 1 \neq 0

is always true on its real domain

⇥Domain of definition:

x \in ℝ

2) Let's compute the integral:

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

ⓘ Differentiating

\arctan (x)

gives

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

, so

\arctan (x)

is an antiderivative of

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

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

\arctan (x)

\arctan (x)

▶An indefinite integral is defined up to an additive constant C; we therefore obtain:

\arctan (x) + C

100% free