What is the integral of x^4(ln(x)-2) ?

The integral of x^4(ln(x)-2) is 1/5 x^5ln(x)-(x^5}{25}-\frac{2x^5)/5+C

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integral of x^4(ln(x)-2)

\int x^{4} (ln (x) - 2) d x

\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25} - \frac{2 x ^{5}}{5} + C

Solution steps

\int x^{4} (ln (x) - 2) d x

Expand

x^{4} (ln (x) - 2) : x^{4} ln (x) - 2 x^{4}

= \int x^{4} ln (x) - 2 x^{4} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{4} ln (x) d x - \int 2 x^{4} d x

\int x^{4} ln (x) d x = \frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25}

\int 2 x^{4} d x = \frac{2 x ^{5}}{5}

= \frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25} - \frac{2 x ^{5}}{5}

Add a constant to the solution

= \frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25} - \frac{2 x ^{5}}{5} + C

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What is the integral of x^4(ln(x)-2) ?
The integral of x^4(ln(x)-2) is 1/5 x^5ln(x)-(x^5}{25}-\frac{2x^5)/5+C