What is the integral from-2 to 0 of 3/((x+1)^{2/9)} ?

The integral from-2 to 0 of 3/((x+1)^{2/9)} is 54/7

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integral from-2 to 0 of 3/((x+1)^{2/9)}

\int_{- 2}^{0} \frac{3}{( x + 1 ) ^{\frac{2}{9}}} d x

\frac{54}{7}

Decimal Notation

7.71428 \dots

Solution steps

\int_{- 2}^{0} \frac{3}{( x + 1 ) ^{\frac{2}{9}}} 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{3}{( x + 1 ) ^{\frac{2}{9}}} d x + \int_{- 1}^{0} \frac{3}{( x + 1 ) ^{\frac{2}{9}}} d x

\int_{- 2}^{- 1} \frac{3}{( x + 1 ) ^{\frac{2}{9}}} d x = - \frac{27 ( - 1 ) ^{\frac{7}{9}}}{7}

\int_{- 1}^{0} \frac{3}{( x + 1 ) ^{\frac{2}{9}}} d x = \frac{27}{7}

= - \frac{27 ( - 1 ) ^{\frac{7}{9}}}{7} + \frac{27}{7}

Simplify

- \frac{27 ( - 1 ) ^{\frac{7}{9}}}{7} + \frac{27}{7} : \frac{54}{7}

= \frac{54}{7}

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What is the integral from-2 to 0 of 3/((x+1)^{2/9)} ?
The integral from-2 to 0 of 3/((x+1)^{2/9)} is 54/7