What is the integral of 3/(80-t) ?

The integral of 3/(80-t) is -3ln|80-t|+C

Popular >

integral of 3/(80-t)

\int \frac{3}{80 - t} d t

- 3 ln ∣ 80 - t ∣ + C

Solution steps

\int \frac{3}{80 - t} d t

Take the constant out:

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

= 3 \cdot \int \frac{1}{80 - t} d t

Apply u-substitution

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

= 3 \cdot \int - \frac{1}{u} d u

Take the constant out:

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

= 3 (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 (- ln ∣ u ∣)

Substitute back

u = 80 - t

= 3 (- ln ∣ 80 - t ∣)

Simplify

= - 3 ln ∣ 80 - t ∣

Add a constant to the solution

= - 3 ln ∣ 80 - t ∣ + C

\frac{\partial}{\partial x} ((x^{2} - 1) (y + 2))

\int_{- 2}^{1} x^{2} + x - 2 d x

\int (2 x (x^{2} + 2)^{2}) d x

t sin (t) + cos (t)

2 t^{2} \frac{d x}{d t} = 3 t x + x^{2}