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)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.