What is the integral of x^5ln(3x) ?

The integral of x^5ln(3x) is 1/6 x^6ln(3x)-(x^6)/(36)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of x^5ln(3x)

\int x^{5} ln (3 x) d x

\frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36} + C

Solution steps

\int x^{5} ln (3 x) d x

Apply Integration By Parts

= \frac{1}{6} x^{6} ln (3 x) - \int \frac{x ^{5}}{6} d x

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= \frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} x^{6} ln (3 x) - \frac{x ^{6}}{36} + C

What is the integral of x^5ln(3x) ?
The integral of x^5ln(3x) is 1/6 x^6ln(3x)-(x^6)/(36)+C