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

The integral of ln(x)x^6 is 1/7 x^7ln(x)-(x^7)/(49)+C

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integral of ln(x)x^6

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

\frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49} + C

Solution steps

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

Apply Integration By Parts

= \frac{1}{7} x^{7} ln (x) - \int \frac{x ^{6}}{7} d x

\int \frac{x ^{6}}{7} d x = \frac{x ^{7}}{49}

= \frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49}

Add a constant to the solution

= \frac{1}{7} x^{7} ln (x) - \frac{x ^{7}}{49} + C

What is the integral of ln(x)x^6 ?
The integral of ln(x)x^6 is 1/7 x^7ln(x)-(x^7)/(49)+C