高数如图,第2题
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高数如图,第2题
![](http://img.wesiedu.com/upload/a/1a/a1a49cf0c2d7ce73c75df1a4b790a0a2.jpg)
![](http://img.wesiedu.com/upload/a/1a/a1a49cf0c2d7ce73c75df1a4b790a0a2.jpg)
![高数如图,第2题](/uploads/image/z/7527043-19-3.jpg?t=%E9%AB%98%E6%95%B0%E5%A6%82%E5%9B%BE%2C%E7%AC%AC2%E9%A2%98%26nbsp%3B)
∫(x^5+x^4-8)/(x^3-x)dx
=∫(x^5-x^3+x^4-x^2+x^3-x+x^2-1+x-1-6)/(x^3-x)dx
=∫(x^2+x+1+1/x+1/x(x+1)-6/(x^3-x))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x))-6S1/(x^3-x)dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3S(1/(x-1)-2/x+1/(x+1))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3ln(x-1)+6lnx-3ln(x+1)+c
=1/3*x^3+1/2*x^2+x+8lnx-4ln(1+x)-3ln(x-1)+c
=∫(x^5-x^3+x^4-x^2+x^3-x+x^2-1+x-1-6)/(x^3-x)dx
=∫(x^2+x+1+1/x+1/x(x+1)-6/(x^3-x))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x))-6S1/(x^3-x)dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3S(1/(x-1)-2/x+1/(x+1))dx
=1/3*x^3+1/2*x^2+x+lnx+ln(x/(1+x)-3ln(x-1)+6lnx-3ln(x+1)+c
=1/3*x^3+1/2*x^2+x+8lnx-4ln(1+x)-3ln(x-1)+c