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

The integral of (ln(2)x^5)/(x^2) is 1/4 ln(2)x^4+C

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integral of (ln(2)x^5)/(x^2)

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

\frac{1}{4} ln (2) x^{4} + C

Solution steps

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

Take the constant out:

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

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

Simplify

\frac{x ^{5}}{x ^{2}} : x^{3}

= ln (2) \cdot \int x^{3} d x

Apply the Power Rule

= ln (2) \frac{x ^{4}}{4}

Simplify

ln (2) \frac{x ^{4}}{4} : \frac{1}{4} ln (2) x^{4}

= \frac{1}{4} ln (2) x^{4}

Add a constant to the solution

= \frac{1}{4} ln (2) x^{4} + C

What is the integral of (ln(2)x^5)/(x^2) ?
The integral of (ln(2)x^5)/(x^2) is 1/4 ln(2)x^4+C