What is the integral from 0 to 5 of 1/(sqrt(7x+3)) ?

The integral from 0 to 5 of 1/(sqrt(7x+3)) is (2sqrt(38)-2sqrt(3))/7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 5 of 1/(sqrt(7x+3))

\int_{0}^{5} \frac{1}{7 x + 3} d x

\frac{2 38 - 2 3}{7}

Decimal

1.26638 \dots

Solution steps

\int_{0}^{5} \frac{1}{7 x + 3} d x

Apply u-substitution

= \int_{3}^{38} \frac{1}{7 u} d u

Take the constant out:

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

= \frac{1}{7} \cdot \int_{3}^{38} \frac{1}{u} d u

Apply the Power Rule

= \frac{1}{7} [2 u^{\frac{1}{2}}]_{3}^{38}

Apply radical rule:

= \frac{1}{7} [2 u]_{3}^{38}

Compute the boundaries:

238 - 23

= \frac{1}{7} (238 - 23)

Simplify

= \frac{2 38 - 2 3}{7}

What is the integral from 0 to 5 of 1/(sqrt(7x+3)) ?
The integral from 0 to 5 of 1/(sqrt(7x+3)) is (2sqrt(38)-2sqrt(3))/7