求解不定积分∫ [lg(x+(x^2+1)^1/2)] dx

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求解不定积分∫[lg(x+(x^2+1)^1/2)]dx求解不定积分∫[lg(x+(x^2+1)^1/2)]dx求解不定积分∫[lg(x+(x^2+1)^1/2)]dxDUIMA?∫ln[x+√(x^

求解不定积分∫ [lg(x+(x^2+1)^1/2)] dx
求解不定积分∫ [lg(x+(x^2+1)^1/2)] dx

求解不定积分∫ [lg(x+(x^2+1)^1/2)] dx
DUIMA?

∫ln[x+√(x^2+1)] dx
=x*ln[x+√(x^2+1)]-∫x dln[x+√(x^2+1)],分部积分法
=xln[x+√(x^2+1)]-∫x/√(x^2+1) dx
=xln[x+√(x^2+1)]-(1/2)∫1/√(x^2+1) d(x^2+1)
=xln[x+√(x^2+1)]-(1/2)*2√(x^2+1)+C
=xln[x+√(x^2+1)]-√(x^2+1)+C