What is the integral from 1 to 2 of (5sqrt(x^2-1))/x ?

The integral from 1 to 2 of (5sqrt(x^2-1))/x is 5(-pi/3+sqrt(3))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 1 to 2 of (5sqrt(x^2-1))/x

\int_{1}^{2} \frac{5 x ^{2} - 1}{x} d x

5 (- \frac{π}{3} + 3)

Decimal

3.42426 \dots

Solution steps

\int_{1}^{2} \frac{5 x ^{2} - 1}{x} d x

Take the constant out:

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

= 5 \cdot \int_{1}^{2} \frac{x ^{2} - 1}{x} d x

Apply u-substitution

= 5 \cdot \int_{0}^{3} \frac{u ^{2}}{u ^{2} + 1} d u

\frac{u ^{2}}{u ^{2} + 1} = - \frac{1}{u ^{2} + 1} + 1

= 5 \cdot \int_{0}^{3} - \frac{1}{u ^{2} + 1} + 1 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

= 5 (- \int_{0}^{3} \frac{1}{u ^{2} + 1} d u + \int_{0}^{3} 1 d u)

\int_{0}^{3} \frac{1}{u ^{2} + 1} d u = \frac{π}{3}

\int_{0}^{3} 1 d u = 3

= 5 (- \frac{π}{3} + 3)

d er i v a t i v e f (x) = x^{2} + 1.8 x - 0.1404

\int cos^{4} (2 x) sin^{3} (2 x) d x

\int x^{21} e^{x^{22}} d x

ma c l a u r in ln^{2} (1 + x)

\int \frac{x ^{15}}{1 + x ^{16}} d x

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