What is the integral of x^7ln(x) ?

The integral of x^7ln(x) is 1/8 x^8ln(x)-(x^8)/(64)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^7ln(x)

\int x^{7} ln (x) d x

\frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64} + C

Solution steps

\int x^{7} ln (x) d x

Apply Integration By Parts

= \frac{1}{8} x^{8} ln (x) - \int \frac{x ^{7}}{8} d x

\int \frac{x ^{7}}{8} d x = \frac{x ^{8}}{64}

= \frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64}

Add a constant to the solution

= \frac{1}{8} x^{8} ln (x) - \frac{x ^{8}}{64} + C

What is the integral of x^7ln(x) ?
The integral of x^7ln(x) is 1/8 x^8ln(x)-(x^8)/(64)+C