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

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

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integral of x^6ln(x)

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

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

Solution steps

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

Apply Integration By Parts

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

= \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

\int e^{3 - x} d x

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\frac{d}{d x} (e^{c o s (x)} \cdot sin (x^{2} - x))

2 x^{2}, 2 x + 6, - 1.3, 2.3

\frac{s}{s ^{2} + 10 s + 25}

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