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Popular >

integral of (x^8)/(x^9-1)

Solution

\int \frac{x ^{8}}{x ^{9} - 1} d x

Solution

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

Solution steps

\int \frac{x ^{8}}{x ^{9} - 1} d x

Apply u-substitution

: \int \frac{1}{9 u} d u

= \int \frac{1}{9 u} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{9} ln ∣ u ∣

Substitute back

u = x^{9} - 1

= \frac{1}{9} ln x^{9} - 1

Add a constant to the solution

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

Popular Examples

integral of (3x^5-8x^3+2)

\int (3 x^{5} - 8 x^{3} + 2) d x

integral of ((x^3-x^4)^2)/(sqrt(x))

\int \frac{( x ^{3} - x ^{4} ) ^{2}}{x} d x

integral of x/2 e^{-(3x)/4}

\int \frac{x}{2} e^{- \frac{3 x}{4}} d x

integral of 1/((3+cos(x)))

\int \frac{1}{( 3 + cos ( x ) )} d x

integral of t^2e^{6t}

\int t^{2} e^{6 t} d t

Frequently Asked Questions (FAQ)

What is the integral of (x^8)/(x^9-1) ?
The integral of (x^8)/(x^9-1) is 1/9 ln|x^9-1|+C