What is the integral of 4/(25-x) ?

The integral of 4/(25-x) is -4ln|25-x|+C

Popular >

integral of 4/(25-x)

\int \frac{4}{25 - x} d x

- 4 ln ∣ 25 - x ∣ + C

Solution steps

\int \frac{4}{25 - x} d x

Take the constant out:

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

= 4 \cdot \int \frac{1}{25 - x} d x

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 = 25 - x

= 4 (- ln ∣ 25 - x ∣)

Simplify

= - 4 ln ∣ 25 - x ∣

Add a constant to the solution

= - 4 ln ∣ 25 - x ∣ + C

f (x) = 294 x^{5} - 120 x^{4} + 420 x^{2}

f (x) = 3 x^{2} + 4 x, at x = - 3

\int \frac{7}{2 y ^{4}} d y

y^{^{'}} = \frac{x ^{4} y ^{4} + 4 x ^{4}}{y ^{3}}

x^{3} + 2 x^{2} + 4