What is the integral of ln(5x+4) ?

The integral of ln(5x+4) is xln(5x+4)+4/5 ln(5x+4)-x-4/5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of ln(5x+4)

\int ln (5 x + 4) d x

x ln (5 x + 4) + \frac{4}{5} ln (5 x + 4) - x - \frac{4}{5} + C

Solution steps

\int ln (5 x + 4) d x

Apply u-substitution

: \int ln (u) \frac{1}{5} d u

= \int ln (u) \frac{1}{5} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int ln (u) d u

Apply Integration By Parts

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

= \frac{1}{5} (u ln (u) - \int 1 d u)

\int 1 d u = u

= \frac{1}{5} (u ln (u) - u)

Substitute back

u = 5 x + 4

= \frac{1}{5} ((5 x + 4) ln (5 x + 4) - (5 x + 4))

Simplify

\frac{1}{5} ((5 x + 4) ln (5 x + 4) - (5 x + 4)) : x ln (5 x + 4) + \frac{4}{5} ln (5 x + 4) - x - \frac{4}{5}

= x ln (5 x + 4) + \frac{4}{5} ln (5 x + 4) - x - \frac{4}{5}

Add a constant to the solution

= x ln (5 x + 4) + \frac{4}{5} ln (5 x + 4) - x - \frac{4}{5} + C

\frac{d}{d x} (\frac{1}{sin ( x )} + \frac{1}{cos ( x )})

\frac{d}{d y} (2 4 - y)

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

\frac{d}{d x} (2 sec (x))

y = 1 + e^{- 2 x^{2} + 8 x - 7}

What is the integral of ln(5x+4) ?
The integral of ln(5x+4) is xln(5x+4)+4/5 ln(5x+4)-x-4/5+C