What is the integral of (-2)/(5t+4) ?

The integral of (-2)/(5t+4) is -2/5 ln|5t+4|+C

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integral of (-2)/(5t+4)

integral

\frac{- 2}{5 t + 4}

- \frac{2}{5} ln ∣ 5 t + 4 ∣ + C

Solution steps

\int \frac{- 2}{5 t + 4} d t

Take the constant out:

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

= - 2 \cdot \int \frac{1}{5 t + 4} d t

Apply u-substitution

= - 2 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= - 2 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 5 t + 4

= - 2 \cdot \frac{1}{5} ln ∣ 5 t + 4 ∣

Simplify

- 2 \cdot \frac{1}{5} ln ∣ 5 t + 4 ∣ : - \frac{2}{5} ln ∣ 5 t + 4 ∣

= - \frac{2}{5} ln ∣ 5 t + 4 ∣

Add a constant to the solution

= - \frac{2}{5} ln ∣ 5 t + 4 ∣ + C

What is the integral of (-2)/(5t+4) ?
The integral of (-2)/(5t+4) is -2/5 ln|5t+4|+C