integrate 1/(x+1) — step-by-step solution

Let's compute the integral:

\int(\frac{1}{x + 1})dx

For the math expression:

\frac{1}{x + 1}

, we know the derivative formula:

{(\ln (a))}^{'} = \frac{1}{a}

, so we try differentiating with ln

Let's differentiate:

{(\ln (x + 1))}^{'}

Apply the differentiation rule:

{(\ln (f))}^{'} = {(f)}^{'} \cdot \frac{1}{f}

with f =

x + 1

{(x + 1)}^{'} \cdot \frac{1}{x + 1}

\frac{1 + 0}{x + 1}

\frac{1}{x + 1}

You observe that the computed derivative and the original math expression are the same, except for a coefficient. So the integral is:

\ln (x + 1)

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

\ln (x + 1) + C

▷Result: $\ln (x + 1) + C$ , with C being any constant