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

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

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

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

ln x^{5} + 4 x + C

Solution steps

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

= ln x^{5} + 4 x

Add a constant to the solution

= ln x^{5} + 4 x + C

\int_{0}^{\frac{π}{4}} sec^{2} (t) d t

\frac{d y}{d x} = \frac{1 - 2 x}{4 x - x ^{2}}

y + 6 y^{3}

f (x) = \frac{x - x ^{2}}{3 x ^{2} + 2}

\int \frac{3 x ^{2}}{5} + \frac{7 x ^{3}}{8} d x

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