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

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

Popular >

integral of x^4ln^2(x)

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

\frac{d}{d x} (\frac{4 x}{x + 4})

y = 8 + 5 x^{2} - 2 x^{3}

\frac{4 s}{( s + 2 ) ^{2}}

\frac{d}{d y} (\frac{x}{y})

\int_{0}^{\frac{π}{12}} tan (6 x) d x

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