What is the integral from-6 to 7 of 9/((3x+5)^{1/3)} ?

The integral from-6 to 7 of 9/((3x+5)^{1/3)} is -(9*13^{2/3})/2+(9*13^{2/3})/(2^{1/3)}

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integral from-6 to 7 of 9/((3x+5)^{1/3)}

\int_{- 6}^{7} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x

- \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2} + \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2 ^{\frac{1}{3}}}

Decimal

14.61423 \dots

Solution steps

\int_{- 6}^{7} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x

Find undefined (singularity) points:

x = - \frac{5}{3}

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_{- 6}^{- \frac{5}{3}} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x + \int_{- \frac{5}{3}}^{7} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x

\int_{- 6}^{- \frac{5}{3}} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x = - \frac{9 ( - 1 ) ^{\frac{2}{3}} \cdot 1 3 ^{\frac{2}{3}}}{2}

\int_{- \frac{5}{3}}^{7} \frac{9}{( 3 x + 5 ) ^{\frac{1}{3}}} d x = \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2 ^{\frac{1}{3}}}

= - \frac{9 ( - 1 ) ^{\frac{2}{3}} \cdot 1 3 ^{\frac{2}{3}}}{2} + \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2 ^{\frac{1}{3}}}

9 (- 1)^{\frac{2}{3}} \cdot 1 3^{\frac{2}{3}} = 9 \cdot 1 3^{\frac{2}{3}}

= - \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2} + \frac{9 \cdot 1 3 ^{\frac{2}{3}}}{2 ^{\frac{1}{3}}}

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What is the integral from-6 to 7 of 9/((3x+5)^{1/3)} ?
The integral from-6 to 7 of 9/((3x+5)^{1/3)} is -(9*13^{2/3})/2+(9*13^{2/3})/(2^{1/3)}