2019-수학-가형-홀수-16¶
문제¶
풀이¶
from sympy import *
x = symbols('x')
val = Rational(1,3)*integrate(1/x+1/x**2,(x,Rational(1,2),2))
val
\[\displaystyle \frac{2 \log{\left(2 \right)}}{3} + \frac{1}{2}\]
풀이2¶
아래의 유리함수 \(f\)는 문제의 조건을 만족한다.
f = Rational(2,3)*x**(-2) + Rational(1,3)*x**(-1) - Rational(1,3)
simplify(2*f+(f.subs(x,1/x))/x**2-(1/x+1/x**2))
\[\displaystyle 0\]
integrate(f,(x,Rational(1,2),2))
\[\displaystyle \frac{2 \log{\left(2 \right)}}{3} + \frac{1}{2}\]