What is the integral of ((ln(x)-3)^2)/(5x) ?

The integral of ((ln(x)-3)^2)/(5x) is 1/15 (ln(x)-3)^3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ((ln(x)-3)^2)/(5x)

\int \frac{( ln ( x ) - 3 ) ^{2}}{5 x} d x

\frac{1}{15} (ln (x) - 3)^{3} + C

Solution steps

\int \frac{( ln ( x ) - 3 ) ^{2}}{5 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{5} \cdot \int \frac{( ln ( x ) - 3 ) ^{2}}{x} d x

Apply u-substitution

: \int u^{2} d u

= \frac{1}{5} \cdot \int u^{2} d u

Apply the Power Rule

: \frac{u ^{3}}{3}

= \frac{1}{5} \cdot \frac{u ^{3}}{3}

Substitute back

u = ln (x) - 3

= \frac{1}{5} \cdot \frac{( ln ( x ) - 3 ) ^{3}}{3}

Simplify

\frac{1}{5} \cdot \frac{( ln ( x ) - 3 ) ^{3}}{3} : \frac{1}{15} (ln (x) - 3)^{3}

= \frac{1}{15} (ln (x) - 3)^{3}

Add a constant to the solution

= \frac{1}{15} (ln (x) - 3)^{3} + C

\int (x + 1) (x^{2} + 2 x + 4) d x

\int (x - 5)^{\frac{1}{2}} d x

\int 5 x + \frac{2}{x} d x

\int \frac{x + 8}{x ^{3} + 48 x - 49} d x

\int (8 z + 4 z^{3} - 6 z^{2}) d z

What is the integral of ((ln(x)-3)^2)/(5x) ?
The integral of ((ln(x)-3)^2)/(5x) is 1/15 (ln(x)-3)^3+C