Question

integrate x5+3x4-x3+8x2-x+8/x2+1the no.s are in power to x like x to power 5 and so on

Answer 1

$I= \int\limits^a_b {(x^5+3x^4-x^3+8x^2-x+\frac{8}{x^2}+1)} \, dx \\\\ \int\limits^a_b {x^n} \, dx = \frac{1}{n+1}x^{n+1}\\\\I=\frac{1}{6}x^6+\frac{3}{5}x^5-\frac{1}{4}x^4+\frac{8}{3}x^3-\frac{1}{2}x^2+8\frac{1}{(-2+1)}x^{-2+1}+\frac{1}{0+1}x^{0+1}+K\\\\=\frac{1}{6}x^6+\frac{3}{5}x^5-\frac{1}{4}x^4+\frac{8}{3}x^3-\frac{1}{2}x^2-\frac{8}{x}+x+K$