What is the integral of x^3ln(8x) ?

The integral of x^3ln(8x) is 1/4 x^4ln(8x)-(x^4)/(16)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^3ln(8x)

\int x^{3} ln (8 x) d x

\frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16} + C

Solution steps

\int x^{3} ln (8 x) d x

Apply Integration By Parts

: \frac{1}{4} x^{4} ln (8 x) - \int \frac{x ^{3}}{4} d x

= \frac{1}{4} x^{4} ln (8 x) - \int \frac{x ^{3}}{4} d x

\int \frac{x ^{3}}{4} d x = \frac{x ^{4}}{16}

= \frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16}

Add a constant to the solution

= \frac{1}{4} x^{4} ln (8 x) - \frac{x ^{4}}{16} + C

x \to - 3 lim (3)

\int \frac{5 ( 4 x + 2 )}{2 ( x ^{2} + 4 x + 5 )} d x

f (x) = \frac{x ^{2}}{( 1 + x )}

n = 1 \sum \infty (1 - \frac{1}{n})^{n}

y = \frac{x}{2 - tan ( x )}

What is the integral of x^3ln(8x) ?
The integral of x^3ln(8x) is 1/4 x^4ln(8x)-(x^4)/(16)+C