What is the integral from 3 to 4 of 6/(3x-8) ?

The integral from 3 to 4 of 6/(3x-8) is 4ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 3 to 4 of 6/(3x-8)

\int_{3}^{4} \frac{6}{3 x - 8} d x

4 ln (2)

Decimal

2.77258 \dots

Solution steps

\int_{3}^{4} \frac{6}{3 x - 8} d x

Take the constant out:

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

= 6 \cdot \int_{3}^{4} \frac{1}{3 x - 8} d x

Apply u-substitution

: \int_{1}^{4} \frac{1}{3 u} d u

= 6 \cdot \int_{1}^{4} \frac{1}{3 u} d u

Take the constant out:

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

= 6 \cdot \frac{1}{3} \cdot \int_{1}^{4} \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 6 \cdot \frac{1}{3} [ln ∣ u ∣]_{1}^{4}

Simplify

6 \cdot \frac{1}{3} [ln ∣ u ∣]_{1}^{4} : 2 [ln ∣ u ∣]_{1}^{4}

= 2 [ln ∣ u ∣]_{1}^{4}

Compute the boundaries:

2 ln (2)

= 2 \cdot 2 ln (2)

Simplify

= 4 ln (2)

\int_{0}^{3} (1) d x

\int_{3}^{4} 4 d x

\int_{3}^{5} e^{- x^{2}} x d x

\int_{0}^{1} (ln (1 + x)) d x

\int_{2}^{3} (3 x^{2} + 2 x) d x

What is the integral from 3 to 4 of 6/(3x-8) ?
The integral from 3 to 4 of 6/(3x-8) is 4ln(2)