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

The integral of-x^4ln(x) is -1/5 x^5ln(x)+(x^5)/(25)+C

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integral of-x^4ln(x)

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

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

Solution steps

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

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

Simplify

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

Add a constant to the solution

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

t^{2} y^{^{''}} - t y^{^{'}} + y = 0

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{3}}{x ^{2} - 4})

\int cos (1) d x

\int \frac{18 x ^{3} - 36 x ^{2} + 5}{x ^{2} - 2 x} d x

\frac{d ^{3}}{d x ^{3}} (x e^{x})

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