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

\frac{y ^{4}}{x ^{12}} + 8 e^{x}

\int_{0}^{5} (x e^{- x}) d x

\frac{d}{d x} (2 + x x)

y = (x^{5} + 1)^{7}

\frac{d y}{d x} - y = 2 e^{x} y^{2}

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