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求不定积分∫1/√2x+3+√2x-1dx

题目详情
求不定积分∫1/√2x+3+√2x-1dx
▼优质解答
答案和解析
∫1/√2x+3+√2x-1dx=∫√2x+3-√2x-1/(√2x+3+√2x-1)(√2x+3-√2x-1)dx
=1/4∫√2x+3dx-1/4∫√2x-1dx
=1/8∫√2x+3d(2x+3)-1/8∫√2x-1d(2x-1)
=1/12(√2x+3)^3-1/12(√2x-1)^3+C
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