Le Mathematique

>>82167

(2/3)x(x+1)^(3/2) - (4/15)(x+1)^(5/2) + c

>find common denominator and split (x+1)^(5/2) using properties of exponents
= (10/15)x(x+1)^(3/2) - (4/15)(x+1)^(2/2)*(x+1)^(3/2) + c

>find common factor between two terms (highlighted using square brackets)
= [(2/15)(x+1)^(3/2)]*5x - [(2/15)(x+1)^(3/2)]*2(x+1)^(2/2) + c

>factor
= (2/15)(x+1)^(3/2) * (5x - 2(x+1)^(2/2)) + c

>2(x+1)^(2/2) reduces to (2x+2)
= (2/15)(x+1)^(3/2) * (5x - 2x - 2) + c

>simplify and rearrange
= (2/15)*(3x-2)*(x+1)^(3/2) + c

>>82195
Not OP but was curious about the question as well because it's been a damn long time since I've done this sort of math

Thanks, anon