求下面两式的不定积分1.sinx/x2.1/lnx
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求下面两式的不定积分
1.sinx/x
2.1/lnx
1.sinx/x
2.1/lnx
![求下面两式的不定积分1.sinx/x2.1/lnx](/uploads/image/z/19881265-49-5.jpg?t=%E6%B1%82%E4%B8%8B%E9%9D%A2%E4%B8%A4%E5%BC%8F%E7%9A%84%E4%B8%8D%E5%AE%9A%E7%A7%AF%E5%88%861.sinx%2Fx2.1%2Flnx)
这个积分可能没有显性的解析式,可以使用无穷级数积分,得到结果:
sinx = x - x^3/(3!) + x^5/(5!) - x^7/(7!) + .
f'(x) = (sinx)/x
= 1 - x^2/(3!) + x^4/(5!) - x^6/(7!) + .
f(x) = x - x^3/(2*3!) + x^5/(4*5!) - x^7/(6*7!) + .
sinx = x - x^3/(3!) + x^5/(5!) - x^7/(7!) + .
f'(x) = (sinx)/x
= 1 - x^2/(3!) + x^4/(5!) - x^6/(7!) + .
f(x) = x - x^3/(2*3!) + x^5/(4*5!) - x^7/(6*7!) + .