What is the integral of 5(ln(x))/x ?

The integral of 5(ln(x))/x is 5/2 ln^2(x)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5(ln(x))/x

\int 5 \frac{ln ( x )}{x} d x

\frac{5}{2} ln^{2} (x) + C

Solution steps

\int 5 \cdot \frac{ln ( x )}{x} d x

Take the constant out:

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

= 5 \cdot \int \frac{ln ( x )}{x} d x

Apply u-substitution

: \int u d u

= 5 \cdot \int u d u

Apply the Power Rule

: \frac{u ^{2}}{2}

= 5 \cdot \frac{u ^{2}}{2}

Substitute back

u = ln (x)

= 5 \cdot \frac{ln ^{2} ( x )}{2}

Simplify

5 \cdot \frac{ln ^{2} ( x )}{2} : \frac{5}{2} ln^{2} (x)

= \frac{5}{2} ln^{2} (x)

Add a constant to the solution

= \frac{5}{2} ln^{2} (x) + C

\int z e^{4 z^{2}} d z

\int \frac{10}{( 3 x - 3 ) ( x ^{2} + 9 )} d x

\int \frac{1}{w ln ( w )} d w

\int cos^{2} (y) sin (y) d y

\int (arccos (x) - ln (x)) d x

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