48. Incorrect. The
answer is true not false. Integration by parts is performed in the
following way. ∫f(x)g'(x)dx = f(x)g(x) - ∫f'(x)g(x)dx. ∫10x(x+1)3dx. Let
g'(x) = (x+1)3, then f'(x) = 10 and g(x) = ∫(x+1)3dx = [(x+1)4]/4+c.
Substitute f(x), f'(x) and g(x): ∫10x(x+1)3dx = 10x*[(x+1)4]/4 - ∫10*[(x+1)4]/4dx
= 2.5x(x+1)4 - 2.5∫(x+1)4dx = 2.5x(x+1)4 - 0.5(x+1)5+c