What is the integral from 0 to t of 1/(t+10) ?

The integral from 0 to t of 1/(t+10) is ln|t+10|-ln(10)

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integral from 0 to t of 1/(t+10)

\int_{0}^{t} \frac{1}{t + 10} d t

ln ∣ t + 10 ∣ - ln (10)

Solution steps

\int_{0}^{t} \frac{1}{t + 10} d t

Apply u-substitution

= \int_{10}^{t + 10} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= [ln ∣ u ∣]_{10}^{t + 10}

Compute the boundaries:

ln ∣ t + 10 ∣ - ln (10)

= ln ∣ t + 10 ∣ - ln (10)

What is the integral from 0 to t of 1/(t+10) ?
The integral from 0 to t of 1/(t+10) is ln|t+10|-ln(10)