What is the right answer?

enter image source here

1 Answer
Mar 1, 2018

The answer is #"option C"=1/54(3x+1)^6+17/45(3x+1)^5+C#

Explanation:

Let #u=3x+1#, #=>#, #3dx=du#

#3x=u-1#

#x=(u-1)/3#

#x+6=(u-1)/3+6=1/3(u+17)#

Therefore,

#int(x+6)(3x+1)^4dx#

#=1/3int(u+17)1/3u^4du#

#=1/9int(u^5+17u^4)du#

#=1/9(u^6/6+17/5u^5)#

#=1/54(3x+1)^6+17/45(3x+1)^5+C#