Intergrate....
1. x^5-2x+5 diveded by x^3 dx
2. √x (1+√x)^3 dx
3. (1-3x)^9 dx
4. sin2xcosxdx
5. x + 2x^3 diveded by (x^4 + x^2)^3 dx
$\displaystyle (x^5-2x+5)/x^3 = x^2 - 2x^{-2} + 5x^{-3}$. Now integrate each term.
Let $\displaystyle \mu = 1+\sqrt{x}$.2. √x (1+√x)^3 dx
Let $\displaystyle \mu = 1-3x$3. (1-3x)^9 dx
Double angle, $\displaystyle 2\sin x\cos^2 x$ and let $\displaystyle \mu = \cos x$.4. sin2xcosxdx
Let $\displaystyle \mu = x^4+x^2$.5. x + 2x^3 diveded by (x^4 + x^2)^3 dx
Do you mean "Can you please work them out completely so I can copy the work and turn it in as my own?"
ThePerfectHacker has given you the all of the problems you have asked, meaning all the thought required has been done for you. Now all you have to do is pretend to be computer and go through the algorithm of integrating basic functions.