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

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

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

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

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

\frac{20}{2} ln (3) = 10 ln (3)

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

Simplify

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 10 ln (3) ln ∣ x ∣

Add a constant to the solution

= 10 ln (3) ln ∣ x ∣ + C

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