What is the integral of ln(9x+4) ?

The integral of ln(9x+4) is xln(9x+4)+4/9 ln(9x+4)-x-4/9+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(9x+4)

\int ln (9 x + 4) d x

x ln (9 x + 4) + \frac{4}{9} ln (9 x + 4) - x - \frac{4}{9} + C

Solution steps

\int ln (9 x + 4) d x

Apply u-substitution

: \int ln (u) \frac{1}{9} d u

= \int ln (u) \frac{1}{9} d u

Take the constant out:

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

= \frac{1}{9} \cdot \int ln (u) d u

Apply Integration By Parts

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

= \frac{1}{9} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{9} (u ln (u) - u)

Substitute back

u = 9 x + 4

= \frac{1}{9} ((9 x + 4) ln (9 x + 4) - (9 x + 4))

Simplify

\frac{1}{9} ((9 x + 4) ln (9 x + 4) - (9 x + 4)) : x ln (9 x + 4) + \frac{4}{9} ln (9 x + 4) - x - \frac{4}{9}

= x ln (9 x + 4) + \frac{4}{9} ln (9 x + 4) - x - \frac{4}{9}

Add a constant to the solution

= x ln (9 x + 4) + \frac{4}{9} ln (9 x + 4) - x - \frac{4}{9} + C

\frac{d}{d x} (\frac{1 - 2 x}{4 + x})

n = 0 \sum \infty 4 (\frac{2}{3})^{2 n}

\int x^{- \frac{7}{4}} d x

f (x) = \frac{x}{2 ( x ^{2} + 7 ) ^{\frac{3}{4}}}

\frac{d}{d x} (sin (5 x + 2))

What is the integral of ln(9x+4) ?
The integral of ln(9x+4) is xln(9x+4)+4/9 ln(9x+4)-x-4/9+C