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Popular >

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

Solution

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

Solution

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

Solution steps

\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

Popular Examples

integral of cos(x)e^{3x}

\int cos (x) e^{3 x} d x

integral of ((x^2)/3+1)ln(2x)

\int (\frac{x ^{2}}{3} + 1) ln (2 x) d x

integral of 1/(sin^2(w)(1-4cot(w)))

\int \frac{1}{sin ^{2} ( w ) ( 1 - 4 cot ( w ) )} d w

integral of sqrt(x^3+3x+1)(x^2+1)

\int x^{3} + 3 x + 1 (x^{2} + 1) d x

integral of 2/x-1

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

Frequently Asked Questions (FAQ)

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