What is the integral from-2 to 7 of 1/((x-1)^{2/3)} ?

The integral from-2 to 7 of 1/((x-1)^{2/3)} is 3*3^{1/3}+3*6^{1/3}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from-2 to 7 of 1/((x-1)^{2/3)}

\int_{- 2}^{7} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

3 \cdot 3^{\frac{1}{3}} + 3 \cdot 6^{\frac{1}{3}}

Decimal

9.77811 \dots

Solution steps

\int_{- 2}^{7} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

Find undefined (singularity) points:

x = 1

If exist

b, a < b < c, f (b) =

undefined

, \int_{a}^{c} f (x) d x = \int_{a}^{b} f (x) d x + \int_{b}^{c} f (x) d x

= \int_{- 2}^{1} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x + \int_{1}^{7} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x

\int_{- 2}^{1} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x = - 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}}

\int_{1}^{7} \frac{1}{( x - 1 ) ^{\frac{2}{3}}} d x = 3 \cdot 6^{\frac{1}{3}}

= - 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} + 3 \cdot 6^{\frac{1}{3}}

Simplify

- 3 (- 1)^{\frac{1}{3}} \cdot 3^{\frac{1}{3}} + 3 \cdot 6^{\frac{1}{3}} : 3 \cdot 3^{\frac{1}{3}} + 3 \cdot 6^{\frac{1}{3}}

= 3 \cdot 3^{\frac{1}{3}} + 3 \cdot 6^{\frac{1}{3}}

\int_{2}^{5} 2^{2 x} d x

\int_{2}^{4} (1 - e) d x

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

\int_{1}^{4} \frac{1}{2 x ( 3 - x )} d x

\int_{0}^{2} x^{2} sin (x^{3}) d x

What is the integral from-2 to 7 of 1/((x-1)^{2/3)} ?
The integral from-2 to 7 of 1/((x-1)^{2/3)} is 3*3^{1/3}+3*6^{1/3}