What is the integral of-(10)/(t+7) ?

The integral of-(10)/(t+7) is -10ln|t+7|+C

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integral of-(10)/(t+7)

\int - \frac{10}{t + 7} d t

- 10 ln ∣ t + 7 ∣ + C

Solution steps

\int - \frac{10}{t + 7} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 10 \cdot \int \frac{1}{t + 7} d t

Apply u-substitution

: \int \frac{1}{u} d u

= - 10 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 10 ln ∣ u ∣

Substitute back

u = t + 7

= - 10 ln ∣ t + 7 ∣

Add a constant to the solution

= - 10 ln ∣ t + 7 ∣ + C

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