What is the integral of 4/(100-t) ?

The integral of 4/(100-t) is -4ln|100-t|+C

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integral of 4/(100-t)

\int \frac{4}{100 - t} d t

- 4 ln ∣ 100 - t ∣ + C

Solution steps

\int \frac{4}{100 - t} d t

Take the constant out:

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

= 4 \cdot \int \frac{1}{100 - t} d t

Apply u-substitution

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

= 4 \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

= 4 (- \int \frac{1}{u} d u)

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 (- ln ∣ u ∣)

Substitute back

u = 100 - t

= 4 (- ln ∣ 100 - t ∣)

Simplify

= - 4 ln ∣ 100 - t ∣

Add a constant to the solution

= - 4 ln ∣ 100 - t ∣ + C

\frac{d}{d x} ((5 + x) ln (x))

x + 1, 0.75

y = e^{x}, y = e^{- 2 x}, x = ln (5)

y = \frac{1}{2}

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