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

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

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

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

Solution steps

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

Apply u-substitution

: \int \frac{ln ( u )}{u} d u

= \int \frac{ln ( u )}{u} d u

Apply u-substitution

: \int v d v

= \int v d v

Apply the Power Rule

: \frac{v ^{2}}{2}

= \frac{v ^{2}}{2}

Substitute back

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

Add a constant to the solution

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

\int \frac{x ^{2}}{( x - 6 ) ( x ^{2} - 36 )} d x

\int 8 e^{t} d t

\int tan^{2} (x) sec^{8} (x) d x

\int 2 8 x d x

\int \frac{15}{1 + 16 r ^{2}} d r

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