What is the integral of (5x^4+6)/(x^5+6x) ?

The integral of (5x^4+6)/(x^5+6x) is ln|x^5+6x|+C

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integral of (5x^4+6)/(x^5+6x)

\int \frac{5 x ^{4} + 6}{x ^{5} + 6 x} d x

ln x^{5} + 6 x + C

Solution steps

\int \frac{5 x ^{4} + 6}{x ^{5} + 6 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^{5} + 6 x

= ln x^{5} + 6 x

Add a constant to the solution

= ln x^{5} + 6 x + C

x \to 5 + lim (\frac{4}{x - 5})

x \to 0 lim (x^{8} - \frac{1}{x})

\frac{d}{d x} (sin^{3} (2 x) - cos (2 x))

\int e^{- v} sin (w v) d v

\frac{d y}{d t} = - \frac{t}{y}, y (0) = 4

What is the integral of (5x^4+6)/(x^5+6x) ?
The integral of (5x^4+6)/(x^5+6x) is ln|x^5+6x|+C