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

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

Solution steps

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

Apply Integration By Parts

: \frac{1}{5} x^{5} ln^{2} (x) - \int \frac{2}{5} x^{4} ln (x) d x

= \frac{1}{5} x^{5} ln^{2} (x) - \int \frac{2}{5} x^{4} ln (x) d x

\int \frac{2}{5} x^{4} ln (x) d x = \frac{2}{5} (\frac{1}{5} x^{5} ln (x) - \frac{x ^{5}}{25})

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

Add a constant to the solution

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

\int \frac{9}{x} + 9 x d x

\int \frac{1}{( x - 3 ) ^{2}} d x

y = 2 sin (π x - y), (1, 0)

y^{^{''}} - 5 y^{^{'}} + 6 y = e^{6 x}

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