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

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

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integral of x^4ln(x^2)

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

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

Solution steps

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

Apply Integration By Parts

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

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

\int \frac{2 x ^{4}}{5} d x = \frac{2 x ^{5}}{25}

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

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

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

Add a constant to the solution

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

f (x) = \frac{3 x - 1}{x + 2}

\frac{4}{t}

\int_{0}^{6} \frac{1}{x - 3} d x

\frac{x ^{2}}{3 x + 1}

\int cos (\frac{nπ x}{2 π}) d x

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