Question

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

Answer 1

The given expression is

`\int (5x^{(4)/(5)}-7x^{-(5)/(9)})dx`

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

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

Now, write them together

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

The correct answer is C