※ 引述《connor70909 (微風)》之銘言:
: ∫ x^3/(4x^2+9)^(3/2) dx
=(1/2) ∫ x^2/(4x^2+9)^(3/2) dx^2 ,set u=x^2
=(1/2) ∫ u/(4u+9)^(3/2) du
=(1/2)(1/4) ∫ [ 1/(4u+9)^(1/2) - 9/(4u+9)^(3/2)] du
=(1/2)(1/4) { (2/4)(4u+9)^(1/2) - [9*(-2)/4]/(4u+9)^(1/2) } +c
=(1/16)(4u+9)^(1/2) + (9/16)/(4u+9)^(1/2) +c
=(1/16)(4(x^2)+9)^(1/2) + (9/16)/(4(x^2)+9)^(1/2) +c
: 範圍是3√3/2 到 0
: 這題好難算喔!!!
: 要怎麼算阿
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