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

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

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

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

ln ∣ x ∣ + C

Solution steps

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

Simplify

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

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

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= ln ∣ x ∣

Add a constant to the solution

= ln ∣ x ∣ + C

x \to \infty lim (\frac{0}{x})

\int \frac{x}{( 6 x ^{2} + 5 ) ^{3}} d x

\frac{\frac{d y}{d x}}{y} = 3

\int x^{2} in x d x

n = 1 \sum \infty 8 n