What is the integral from 0 to 1 of (x^9)/(x^{10)-1} ?

The integral from 0 to 1 of (x^9)/(x^{10)-1} is diverges

Popular >

integral from 0 to 1 of (x^9)/(x^{10)-1}

\int_{0}^{1} \frac{x ^{9}}{x ^{10} - 1} d x

diverges

Solution steps

\int_{0}^{1} \frac{x ^{9}}{x ^{10} - 1} d x

Apply u-substitution

: \int_{- 1}^{0} \frac{1}{10 u} d u

= \int_{- 1}^{0} \frac{1}{10 u} d u

Take the constant out:

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

= \frac{1}{10} \cdot \int_{- 1}^{0} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{10} [ln ∣ u ∣]_{- 1}^{0}

Compute the boundaries:

diverges

= diverges

\frac{d}{d x} (sin (x) - cos (x))

\frac{d}{d x} (3 x^{2} + 5 x - 6)

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

\int \frac{3 x ^{3} + x}{x ^{4} + 2 x ^{2} + 1} d x

\frac{1}{( s ^{2} + 3 ) ( s ^{2} + 1 )}

What is the integral from 0 to 1 of (x^9)/(x^{10)-1} ?
The integral from 0 to 1 of (x^9)/(x^{10)-1} is diverges