What is the integral of (4x^3)/(x^4) ?

The integral of (4x^3)/(x^4) is 4ln|x|+C

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integral of (4x^3)/(x^4)

\int \frac{4 x ^{3}}{x ^{4}} d x

4 ln ∣ x ∣ + C

Solution steps

\int \frac{4 x ^{3}}{x ^{4}} d x

Take the constant out:

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

= 4 \cdot \int \frac{x ^{3}}{x ^{4}} d x

Simplify

\frac{x ^{3}}{x ^{4}} : \frac{1}{x}

= 4 \cdot \int \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 4 ln ∣ x ∣

Add a constant to the solution

= 4 ln ∣ x ∣ + C

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