What is the integral of (x^2)/(x(x-4)) ?

The integral of (x^2)/(x(x-4)) is x-4+4ln|x-4|+C

Popular >

integral of (x^2)/(x(x-4))

\int \frac{x ^{2}}{x ( x - 4 )} d x

x - 4 + 4 ln ∣ x - 4 ∣ + C

Solution steps

\int \frac{x ^{2}}{x ( x - 4 )} d x

Apply u-substitution

: \int \frac{u + 4}{u} d u

= \int \frac{u + 4}{u} d u

Expand

\frac{u + 4}{u} : 1 + \frac{4}{u}

= \int 1 + \frac{4}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 1 d u + \int \frac{4}{u} d u

\int 1 d u = u

\int \frac{4}{u} d u = 4 ln ∣ u ∣

= u + 4 ln ∣ u ∣

Substitute back

u = x - 4

= x - 4 + 4 ln ∣ x - 4 ∣

Add a constant to the solution

= x - 4 + 4 ln ∣ x - 4 ∣ + C

\int 2 x x + 4 d x

\int \frac{x ^{5}}{x ^{6} - 5} d x

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

\int 4 x^{- 7} d x

\int \frac{x - 1}{4 - x ^{2}} d x

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