Question

any easy method??(integration)

Answer 1

Answer:

2/5 (x+2) ⁵/₂ - 4/2 (x+2) ³/₂ + C

Step-by-step explanation:

∫ x√x+2 dx

∫ (x+2-2) (x+2)¹/₂ dx       [ADDING AND SUBTRACTING 2]

∫ (x+2)¹ (x+2)¹/² dx - 2∫ (x+2)¹/₂ dx

∫ (x+2)³/₂ dx - 2∫ (x+2)¹/₂ dx

2/5 (x+2)⁵/₂ - 2 (2/3) [x+2]³/₂ + C

2/5 (x+2)⁵/₂ - 4/3 (x+2)³/₂ + C ----- THE ANSWER.