What is the integral of (20x^4)/(2x^5ln(3)) ?

The integral of (20x^4)/(2x^5ln(3)) is (10)/(ln(3))ln|x|+C

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integral of (20x^4)/(2x^5ln(3))

\int \frac{20 x ^{4}}{2 x ^{5} ln ( 3 )} d x

\frac{10}{ln ( 3 )} ln ∣ x ∣ + C

Solution steps

\int \frac{20 x ^{4}}{2 x ^{5} ln ( 3 )} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{20}{2 ln ( 3 )} \cdot \int \frac{x ^{4}}{x ^{5}} d x

Simplify

= \frac{10}{ln ( 3 )} \cdot \int \frac{x ^{4}}{x ^{5}} d x

Simplify

\frac{x ^{4}}{x ^{5}} : \frac{1}{x}

= \frac{10}{ln ( 3 )} \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= \frac{10}{ln ( 3 )} ln ∣ x ∣

Add a constant to the solution

= \frac{10}{ln ( 3 )} ln ∣ x ∣ + C

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What is the integral of (20x^4)/(2x^5ln(3)) ?
The integral of (20x^4)/(2x^5ln(3)) is (10)/(ln(3))ln|x|+C