求此题不定积分 :∫e^x/(e^2x-1)dx
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求此题不定积分 :∫e^x/(e^2x-1)dx
![求此题不定积分 :∫e^x/(e^2x-1)dx](/uploads/image/z/15796853-53-3.jpg?t=%E6%B1%82%E6%AD%A4%E9%A2%98%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%86+%EF%BC%9A%E2%88%ABe%5Ex%2F%28e%5E2x-1%29dx)
原式=∫de^x/(e^x+1)(e^x-1)
=1/2*∫[1/(e^x-1)-1/(e^x+1)]de^x
=1/2*[ln|e^x-1|-1ln(e^x+1)]+C
=1/2*ln[|e^x-1|/(e^x+1)]+C
=1/2*∫[1/(e^x-1)-1/(e^x+1)]de^x
=1/2*[ln|e^x-1|-1ln(e^x+1)]+C
=1/2*ln[|e^x-1|/(e^x+1)]+C