What is the integral of x^5ln|x| ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^5ln|x|

\int x^{5} ln ∣ x ∣ d x

\frac{1}{6} x^{6} ln ∣ x ∣ - \frac{x ^{6}}{36} + C

Solution steps

\int x^{5} ln ∣ x ∣ d x

Apply Integration By Parts

: \frac{1}{6} x^{6} ln ∣ x ∣ - \int \frac{x ^{5}}{6} d x

= \frac{1}{6} x^{6} ln ∣ 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 ∣ x ∣ - \frac{x ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} x^{6} ln ∣ x ∣ - \frac{x ^{6}}{36} + C

\frac{\partial}{\partial y} (1 + x^{2} + y^{2})

\int (3 x^{2} + 2) d x

\int_{0}^{1} 6 x^{2} (3 - 5 x^{3})^{3} d x

- \frac{1}{2} x^{2} - \frac{5}{2} x - 2, [- 2, 7]

\int \frac{1}{x I n x} d x

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