What is the integral of x^5ln(x^2) ?

The integral of x^5ln(x^2) is 1/3 x^6ln(x)-(x^6)/(18)+C

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integral of x^5ln(x^2)

\int x^{5} ln (x^{2}) d x

\frac{1}{3} x^{6} ln (x) - \frac{x ^{6}}{18} + C

Solution steps

\int x^{5} ln (x^{2}) d x

Apply Integration By Parts

: \frac{1}{6} x^{6} ln (x^{2}) - \int \frac{x ^{5}}{3} d x

= \frac{1}{6} x^{6} ln (x^{2}) - \int \frac{x ^{5}}{3} d x

\int \frac{x ^{5}}{3} d x = \frac{x ^{6}}{18}

= \frac{1}{6} x^{6} ln (x^{2}) - \frac{x ^{6}}{18}

\frac{1}{6} x^{6} ln (x^{2}) = \frac{1}{3} x^{6} ln (x)

= \frac{1}{3} x^{6} ln (x) - \frac{x ^{6}}{18}

Add a constant to the solution

= \frac{1}{3} x^{6} ln (x) - \frac{x ^{6}}{18} + C

\int \frac{( x ^{5} )}{1 + x ^{12}} d x

\int \frac{( x ^{2} + 1 ) e ^{x}}{( x + 1 ) ^{2}} d x

\int (x - csc^{2} (x)) d x

\int \frac{x ^{2} + 1}{x ^{\frac{5}{2}}} d x

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

What is the integral of x^5ln(x^2) ?
The integral of x^5ln(x^2) is 1/3 x^6ln(x)-(x^6)/(18)+C