What is the integral of 5/(6+5x) ?

The integral of 5/(6+5x) is ln|6+5x|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(6+5x)

\int \frac{5}{6 + 5 x} d x

ln ∣ 6 + 5 x ∣ + C

Solution steps

\int \frac{5}{6 + 5 x} d x

Take the constant out:

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

= 5 \cdot \int \frac{1}{6 + 5 x} d x

Apply u-substitution

: \int \frac{1}{5 u} d u

= 5 \cdot \int \frac{1}{5 u} d u

Take the constant out:

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

= 5 \cdot \frac{1}{5} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 \cdot \frac{1}{5} ln ∣ u ∣

Substitute back

u = 6 + 5 x

= 5 \cdot \frac{1}{5} ln ∣ 6 + 5 x ∣

Simplify

5 \cdot \frac{1}{5} ln ∣ 6 + 5 x ∣ : ln ∣ 6 + 5 x ∣

= ln ∣ 6 + 5 x ∣

Add a constant to the solution

= ln ∣ 6 + 5 x ∣ + C

\int \frac{1 - x ^{2}}{x ^{4}} d x

(x, y) \to (0, 0) lim (x y^{2})

\int \frac{1}{x 4 x ^{2} + 9} d x

\frac{d}{d x} (4 x - 3)

(x + 2 y^{2}) \cdot d x + x y \cdot d y = 0