**48. Correct. The
answer is true.** 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)^{3}dx. Let
g'(x) = (x+1)^{3}, then f'(x) = 10 and g(x) = ∫(x+1)^{3}dx = [(x+1)^{4}]/4+c.
Substitute f(x), f'(x) and g(x): ∫10x(x+1)^{3}dx = 10x*[(x+1)^{4}]/4 - ∫10*[(x+1)^{4}]/4dx
= 2.5x(x+1)^{4 }- 2.5∫(x+1)^{4}dx = 2.5x(x+1)^{4 }- 0.5(x+1)^{5}+c.