What is the integral of ln(3x-7) ?

The integral of ln(3x-7) is xln(3x-7)-7/3 ln(3x-7)-x+7/3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(3x-7)

\int ln (3 x - 7) d x

x ln (3 x - 7) - \frac{7}{3} ln (3 x - 7) - x + \frac{7}{3} + C

Solution steps

\int ln (3 x - 7) d x

Apply u-substitution

: \int ln (u) \frac{1}{3} d u

= \int ln (u) \frac{1}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int ln (u) d u

Apply Integration By Parts

: u ln (u) - \int 1 d u

= \frac{1}{3} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{3} (u ln (u) - u)

Substitute back

u = 3 x - 7

= \frac{1}{3} ((3 x - 7) ln (3 x - 7) - (3 x - 7))

Simplify

\frac{1}{3} ((3 x - 7) ln (3 x - 7) - (3 x - 7)) : x ln (3 x - 7) - \frac{7}{3} ln (3 x - 7) - x + \frac{7}{3}

= x ln (3 x - 7) - \frac{7}{3} ln (3 x - 7) - x + \frac{7}{3}

Add a constant to the solution

= x ln (3 x - 7) - \frac{7}{3} ln (3 x - 7) - x + \frac{7}{3} + C

\int 2 ln (x) \cdot \frac{1}{x} d x

\int 5 x cos^{2} (x) d x

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

\int \frac{1}{x ^{2} \cdot 4 + x ^{2}} d x

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

What is the integral of ln(3x-7) ?
The integral of ln(3x-7) is xln(3x-7)-7/3 ln(3x-7)-x+7/3+C