integral of (x+1)/x — step-by-step solution

Let's compute the integral:

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

For

x

≠ 0, divide each numerator term by the power in the denominator:

\frac{x + 1}{x} = 1 + \frac{1}{x}

ⅰ

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

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

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

ⓘ The derivative of

x

1

, so

x

is an antiderivative of

1

\int 1 d x

x

■The derivative of

\ln | x |

\frac{1}{x}

, so

\ln | x |

is an antiderivative of

\frac{1}{x}

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

\ln | x |

x + \ln | x |

▶Indefinite integrals are defined up to an additive constant C, so this yields:

x + \ln | x | + C