integrate 1/x

1) Let's find the domain of

\frac{1}{x}

⇥ For the expression

\frac{1}{x}

to be defined, we must have:

x \neq 0

⇥Domain of definition:

x \neq 0

2) Let's integrate:

\int \frac{1}{x} d x

ⓘ Differentiating

\ln | x |

gives

\frac{1}{x}

, so

\ln | x |

is an antiderivative of

\frac{1}{x}

\int \frac{1}{x} d x

\ln | x |

\ln | x |

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

\ln | x | + C

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