1.

Evaluate: ∫(2x + 3)(x2 + 3x + 5)3/2dx.

Answer»

Substituting x2 – 3x + 5 = t to get (2x + 3)dx = dt 

∴ Given integral becomes ∫t3/2dt 

Integrating to get t52/52 + C = 2/5(x2 + 3x + 5)52 + C



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