What is the integral of 5/(8y-7) ?

The integral of 5/(8y-7) is 5/8 ln|8y-7|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 5/(8y-7)

\int \frac{5}{8 y - 7} d y

\frac{5}{8} ln ∣ 8 y - 7 ∣ + C

Solution steps

\int \frac{5}{8 y - 7} d y

Take the constant out:

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

= 5 \cdot \int \frac{1}{8 y - 7} d y

Apply u-substitution

: \int \frac{1}{8 u} d u

= 5 \cdot \int \frac{1}{8 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}{8} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 \cdot \frac{1}{8} ln ∣ u ∣

Substitute back

u = 8 y - 7

= 5 \cdot \frac{1}{8} ln ∣ 8 y - 7 ∣

Simplify

5 \cdot \frac{1}{8} ln ∣ 8 y - 7 ∣ : \frac{5}{8} ln ∣ 8 y - 7 ∣

= \frac{5}{8} ln ∣ 8 y - 7 ∣

Add a constant to the solution

= \frac{5}{8} ln ∣ 8 y - 7 ∣ + C

\int \frac{( ln ( x ) + 2 )}{x} d x

\int x^{3} \cdot arctan (x) d x

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

\int x (5 - 2 x)^{\frac{1}{3}} d x

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