What is the integral from 2 to 6 of x/(sqrt(2x-3)) ?

The integral from 2 to 6 of x/(sqrt(2x-3)) is 22/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 6 of x/(sqrt(2x-3))

\int_{2}^{6} \frac{x}{2 x - 3} d x

\frac{22}{3}

Decimal

7.33333 \dots

Solution steps

\int_{2}^{6} \frac{x}{2 x - 3} d x

Apply u-substitution

= \int_{1}^{3} \frac{u ^{2} + 3}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{3} u^{2} + 3 d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \frac{1}{2} (\int_{1}^{3} u^{2} d u + \int_{1}^{3} 3 d u)

\int_{1}^{3} u^{2} d u = \frac{26}{3}

\int_{1}^{3} 3 d u = 6

= \frac{1}{2} (\frac{26}{3} + 6)

Simplify

\frac{1}{2} (\frac{26}{3} + 6) : \frac{22}{3}

= \frac{22}{3}

What is the integral from 2 to 6 of x/(sqrt(2x-3)) ?
The integral from 2 to 6 of x/(sqrt(2x-3)) is 22/3