How do you integrate #int 2x^2sqrt(x^3+1)dx# from [1,2]?
1 Answer
Jan 25, 2017
Explanation:
This is a substitution problem. Let
#int_1^2 2x^2sqrt(u) * (du)/(3x^2)#
#int_1^2 2/3sqrt(u) du#
#2/3int_1^2 sqrt(u)du#
#2/3[2/3u^(3/2)]_1^2#
#2/3[2/3(x^3 + 1)^(3/2)]_1^2#
#2/3[2/3(2^3 + 1)^(3/2) - 2/3(1^3 +1)^(3/2)]#
#2/3[2/3(27) - 2/3sqrt(8)]#
#2/3[18 - 4/3sqrt(2)]#
#12 - 8/9sqrt(2)#
Hopefully this helps!
