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Calculate the following integral ∫ 〖(5x〗 ^ (4/5) 8- 〖7x〗 ^ (- 5/9)) dx (hint: leave procedure) a) = x^(4/5)-x^(-5/9) + c b) = 〖5x〗^(4/5)/5-〖7x〗^(-5/9)/9 + c c) = 〖5x〗^(9/5)/(9/5)-〖7x〗^(4/9)/(4/9) + c

Calculate the following integral 5x 45 8 7x 59 dx hint leave procedure a x45x59 c b 5x4557x599 c c 5x95957x4949 c class=

Respuesta :

The given expression is

[tex]\int (5x^{\frac{4}{5}}-7x^{-\frac{5}{9}})dx[/tex]

To make the integration add the power by 1 and divide the term by the new power

[tex]\begin{gathered} \int 5x^{\frac{4}{5}}dx=\frac{5x^{\frac{4}{5}+1}}{(\frac{4}{5}+1)}=\frac{5x^{\frac{9}{5}}}{\frac{9}{5}} \\ \int 7x^{-\frac{5}{9}}dx=\frac{7x^{-\frac{5}{9}+1}}{(-\frac{5}{9}+1)}=\frac{7x^{\frac{4}{9}}}{\frac{4}{9}} \end{gathered}[/tex]

Now, write them together

[tex]\int (5x^{\frac{4}{5}}-7x^{-\frac{5}{9}})dx=\frac{5x^{\frac{9}{5}}}{\frac{9}{5}}-\frac{7x^{\frac{4}{9}}}{\frac{4}{9}}+c[/tex]

The correct answer is C

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