Question

Integration of 3x⁴+7x-11/x³​

Answer 1

3x^5/5+7x^2/2-11/2x^2+C

Answer 2

Answer:
`(3)/(2)x^(2)-(7)/(x)+(11)/(2x^2)+C`

Explanation:

`\int {(3x^4+7x-11)/(x^3)} \, dx \\\\\\= \int \bigg({(3x^4)/(x^3)} +(7x)/(x^3)+(-11)/(x^3)\bigg)\, dx\\\\\\= \int \bigg(3x+7x^(-2)-11x^(-3)\bigg)\, dx\\\\\\=(3x^(1+1))/(1+1)+(7x^(-2+1))/(-2+1)+(-11x^(-3+1))/(-3+1)+C\\\\\\=(3x^(2))/(2)+(7x^(-1))/(-1)+(-11x^(-2))/(-2)+C\\\\\\=\large\boxed{(3x^(2))/(2)-(7)/(x)+(11)/(2x^2)+C}`