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Find the integral from 0 to e3-1 of 1/(1+t)

by RoRi

Evaluate the following integral

    \[ \int_0^{e^3-1} \frac{dt}{1+t}. \]

We use the formula for the integral of \frac{1}{t} (and if you want to be thorough we use substitution with u = 1+t and du = dt, but I’ll probably stop writing out that step on routine substitutions).

    \begin{align*} \int_0^{e^3 -1} \frac{dt}{1+t} &= \log |1+t| \Big \rvert_0^{e^3-1} \\ &= \log e^3 - \log 1 \\ &= 3. \end{align*}

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