Verified answer

You may have a mistake in the first one -- see:

http://www.wolframalpha.com/input/?i=integral+x*sq...

and you will see it probably too complicated to do by hand in a reasonable length of time.

But for the second one, you can probably do it. Just go to this link and click "show steps"

http://www.wolframalpha.com/input/?i=integral+sqrt...

1/

int by parts

---->(27/2)ln(√(x^2 +6x) +x+3)+(1/3)(x^2+6x)^(3/2)-(3/2)(x+3)√(x^2 +6x) + C

((-3 + x) x (6 + x) (9 + 2 x) +

162 Sqrt[x] Sqrt[6 + x] ArcSinh[Sqrt[x]/Sqrt[6]])/(6 Sqrt[x (6 + x)])

Merry Christmas.

http://www.wolframalpha.com/input/?i=integral&a=*C...

http://www.wolframalpha.com/input/?i=integral&a=*C...