20163315 유리함수적분

1842 days 전, qogustlr7 작성

유리합수의 적분 25.

f=(4*x)/(x^3+x^2+x+1) fp=f.partial_fraction(x) fp 
       
2*(x + 1)/(x^2 + 1) - 2/(x + 1)
2*(x + 1)/(x^2 + 1) - 2/(x + 1)
integral(fp, x) 
       
2*arctan(x) + log(x^2 + 1) - 2*log(x + 1)
2*arctan(x) + log(x^2 + 1) - 2*log(x + 1)

유리합수의 적분 26.

f=(x^2+x+1)/((x^2+1)^2) fp=f.partial_fraction(x) fp 
       
1/(x^2 + 1) + x/(x^2 + 1)^2
1/(x^2 + 1) + x/(x^2 + 1)^2
integral(fp, x) 
       
-1/2/(x^2 + 1) + arctan(x)
-1/2/(x^2 + 1) + arctan(x)

유리함수의 적분 27.

f=(x^3+x^2+2*x+1)/((x^2+1)*(x^2+2)) fp=f.partial_fraction(x) fp 
       
x/(x^2 + 1) + 1/(x^2 + 2)
x/(x^2 + 1) + 1/(x^2 + 2)
integral(fp, x) 
       
1/2*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/2*log(x^2 + 1)
1/2*sqrt(2)*arctan(1/2*sqrt(2)*x) + 1/2*log(x^2 + 1)

유리함수의 적분 28.

f=(x^2-2*x-1)/((x-1)^2*(x^2+1)) fp=f.partial_fraction(x) fp 
       
-(x - 1)/(x^2 + 1) + 1/(x - 1) - 1/(x - 1)^2
-(x - 1)/(x^2 + 1) + 1/(x - 1) - 1/(x - 1)^2
integral(fp, x) 
       
1/(x - 1) + arctan(x) - 1/2*log(x^2 + 1) + log(x - 1)
1/(x - 1) + arctan(x) - 1/2*log(x^2 + 1) + log(x - 1)