What is the integral of (35x^4-3)/(7x^5-3x) ?

The integral of (35x^4-3)/(7x^5-3x) is ln|7x^5-3x|+C

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integral of (35x^4-3)/(7x^5-3x)

\int \frac{35 x ^{4} - 3}{7 x ^{5} - 3 x} d x

ln 7 x^{5} - 3 x + C

Solution steps

\int \frac{35 x ^{4} - 3}{7 x ^{5} - 3 x} d x

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 7 x^{5} - 3 x

= ln 7 x^{5} - 3 x

Add a constant to the solution

= ln 7 x^{5} - 3 x + C

What is the integral of (35x^4-3)/(7x^5-3x) ?
The integral of (35x^4-3)/(7x^5-3x) is ln|7x^5-3x|+C