What is the integral of (X^2)/(X(X^2-9)) ?

The integral of (X^2)/(X(X^2-9)) is 1/2 ln|X^2-9|+C

Popular >

integral of (X^2)/(X(X^2-9))

\int \frac{X ^{2}}{X ( X ^{2} - 9 )} d X

\frac{1}{2} ln X^{2} - 9 + C

Solution steps

\int \frac{X ^{2}}{X ( X ^{2} - 9 )} d X

Cancel the common factor:

X

= \int \frac{X}{X ^{2} - 9} d X

Apply u-substitution

: \int \frac{1}{2 u} d u

= \int \frac{1}{2 u} d u

Take the constant out:

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} ln ∣ u ∣

Substitute back

u = X^{2} - 9

= \frac{1}{2} ln X^{2} - 9

Add a constant to the solution

= \frac{1}{2} ln X^{2} - 9 + C

\int csc^{2} (6 x) cot (6 x) d x

\int e^{5 x} (e^{5 x} + 2)^{7} d x

\int \frac{x ^{2}}{x ^{2} + 6} d x

\int 2 x + ln (x) d x

\int \frac{2 x - 7}{x ^{2} + 9} d x

What is the integral of (X^2)/(X(X^2-9)) ?
The integral of (X^2)/(X(X^2-9)) is 1/2 ln|X^2-9|+C