What is the integral of x^4ln(5x) ?

The integral of x^4ln(5x) is 1/5 x^5ln(5x)-(x^5)/(25)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^4ln(5x)

\int x^{4} ln (5 x) d x

\frac{1}{5} x^{5} ln (5 x) - \frac{x ^{5}}{25} + C

Solution steps

\int x^{4} ln (5 x) d x

Apply Integration By Parts

: \frac{1}{5} x^{5} ln (5 x) - \int \frac{x ^{4}}{5} d x

= \frac{1}{5} x^{5} ln (5 x) - \int \frac{x ^{4}}{5} d x

\int \frac{x ^{4}}{5} d x = \frac{x ^{5}}{25}

= \frac{1}{5} x^{5} ln (5 x) - \frac{x ^{5}}{25}

Add a constant to the solution

= \frac{1}{5} x^{5} ln (5 x) - \frac{x ^{5}}{25} + C

(ln (x^{3}))^{^{'}}

\frac{1}{( s - 1 ) ( s ^{2} - 1 )}

\int x^{5} x^{3} + 5 d x

\int \frac{( x ^{3} + 64 )}{x ^{2} + 64} d x

\frac{1}{s ( s ^{2} + 34.5 s + 1000 )}

What is the integral of x^4ln(5x) ?
The integral of x^4ln(5x) is 1/5 x^5ln(5x)-(x^5)/(25)+C