What is the integral of x*ln(x^6) ?

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

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integral of x*ln(x^6)

\int x \cdot ln (x^{6}) d x

3 x^{2} ln (x) - \frac{3 x ^{2}}{2} + C

Solution steps

\int x ln (x^{6}) d x

Apply Integration By Parts

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

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

\int 3 x d x = \frac{3 x ^{2}}{2}

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

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

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

Add a constant to the solution

= 3 x^{2} ln (x) - \frac{3 x ^{2}}{2} + C

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