What is the integral of ln(5x+2) ?

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

\int ln (5 x + 2) d x

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

Solution steps

\int ln (5 x + 2) 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 + 2

= \frac{1}{5} ((5 x + 2) ln (5 x + 2) - (5 x + 2))

Simplify

\frac{1}{5} ((5 x + 2) ln (5 x + 2) - (5 x + 2)) : x ln (5 x + 2) + \frac{2}{5} ln (5 x + 2) - x - \frac{2}{5}

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

Add a constant to the solution

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

\int 2 x (1 + x^{2})^{9} d x

\int \frac{3}{9 x ^{2} - 1} d x

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

\frac{1}{y ^{2}}

\int \frac{1 + e ^{- 2 x}}{e ^{- 3 x}} d x

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