Question

Integration of 3x⁴+7x-11/x³​

Answer 1

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

Answer 2

Answer:   $\dfrac{3}{2}x^{2}-\dfrac{7}{x}+\dfrac{11}{2x^2}+C$

Step-by-step explanation:

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