What is the integral of (8x^7+2x)/(x^8+x^2) ?

The integral of (8x^7+2x)/(x^8+x^2) is ln|x^8+x^2|+C

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integral of (8x^7+2x)/(x^8+x^2)

\int \frac{8 x ^{7} + 2 x}{x ^{8} + x ^{2}} d x

ln x^{8} + x^{2} + C

Solution steps

\int \frac{8 x ^{7} + 2 x}{x ^{8} + x ^{2}} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x^{8} + x^{2}

= ln x^{8} + x^{2}

Add a constant to the solution

= ln x^{8} + x^{2} + C

\frac{\partial}{\partial y} (\frac{2 x}{y ^{2}})

y^{^{'}} = 8 (y^{2} + 1)

\int x tan (x^{2} - 1) d x

\int x x^{2} + 8 d x

x \to 0 lim (ln (x - 1))

What is the integral of (8x^7+2x)/(x^8+x^2) ?
The integral of (8x^7+2x)/(x^8+x^2) is ln|x^8+x^2|+C