您给的答案1.设f(x)=∫1到x (Int/1+t)dt ,(x>0),求f(x)+f(1/x)1.f(x)+f(1/x)=∫(1,x)[lnt/(1+t)]dt+∫(1,1/x)[lnt/(1+t)]dt=∫(1,x)[lnt/(1+t)]dt+∫(1,x)[ln(1/t)/(1+1/t)]d(1/t) (第二个积分用1/t代换t)=∫(1,x)[lnt/(1+t)]dt+∫(1,x)[-lnt/(1
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![您给的答案1.设f(x)=∫1到x (Int/1+t)dt ,(x>0),求f(x)+f(1/x)1.f(x)+f(1/x)=∫(1,x)[lnt/(1+t)]dt+∫(1,1/x)[lnt/(1+t)]dt=∫(1,x)[lnt/(1+t)]dt+∫(1,x)[ln(1/t)/(1+1/t)]d(1/t) (第二个积分用1/t代换t)=∫(1,x)[lnt/(1+t)]dt+∫(1,x)[-lnt/(1](/uploads/image/z/13873272-24-2.jpg?t=%E6%82%A8%E7%BB%99%E7%9A%84%E7%AD%94%E6%A1%881.%E8%AE%BEf%28x%29%3D%E2%88%AB1%E5%88%B0x+%28Int%2F1%2Bt%29dt+%2C%28x%3E0%29%2C%E6%B1%82f%28x%29%2Bf%281%2Fx%291.f%28x%29%2Bf%281%2Fx%29%3D%E2%88%AB%281%2Cx%29%5Blnt%2F%281%2Bt%29%5Ddt%2B%E2%88%AB%281%2C1%2Fx%29%5Blnt%2F%281%2Bt%29%5Ddt%3D%E2%88%AB%281%2Cx%29%5Blnt%2F%281%2Bt%29%5Ddt%2B%E2%88%AB%281%2Cx%29%5Bln%281%2Ft%29%2F%281%2B1%2Ft%29%5Dd%281%2Ft%29+%28%E7%AC%AC%E4%BA%8C%E4%B8%AA%E7%A7%AF%E5%88%86%E7%94%A81%2Ft%E4%BB%A3%E6%8D%A2t%29%3D%E2%88%AB%281%2Cx%29%5Blnt%2F%281%2Bt%29%5Ddt%2B%E2%88%AB%281%2Cx%29%5B-lnt%2F%281)
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