What is the integral of (7x^6+8)/(x^7+8x) ?

The integral of (7x^6+8)/(x^7+8x) is ln|x^7+8x|+C

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integral of (7x^6+8)/(x^7+8x)

\int \frac{7 x ^{6} + 8}{x ^{7} + 8 x} d x

ln x^{7} + 8 x + C

Solution steps

\int \frac{7 x ^{6} + 8}{x ^{7} + 8 x} 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^{7} + 8 x

= ln x^{7} + 8 x

Add a constant to the solution

= ln x^{7} + 8 x + C

\int_{1}^{e^{5}} x^{5} ln (x) d x

\frac{\partial}{\partial x} (80 x^{\frac{1}{2}} z^{\frac{1}{2}})

y = x^{2}, y = 2 x + 3

\int_{0}^{8} \frac{7}{3} x d x

x \to 0 lim (\frac{2}{3 cos ( x )})

What is the integral of (7x^6+8)/(x^7+8x) ?
The integral of (7x^6+8)/(x^7+8x) is ln|x^7+8x|+C