This problem requires calculus and is intended only for advanced classes. Let the symbol 'Integral(dx, f(x))' stand for the indefinite integral of the function f(x) with respect to x. It might be easier to understand if it is handwritten in traditional notation. Examine the integration of f(x)=1/x with respect to x, integrating by parts. We can show that 0 is equal to 1.
Integrating f(x)=1/x by parts, use u=1/x and
dv=dx. Thus:
u=1/x and dv=dx
imply
du= -1/(x^2) * dx and v = x
Putting the pieces back together, we find
Integral(dx, 1/x) = u*v - Integral(v*du) Integral(dx, 1/x) = (1/x)*(x) - Integral(dx, x*(-1/(x^2))) Integral(dx, 1/x) = 1 - Integral(dx, -1/x) Integral(dx, 1/x) = 1 + Integral(dx, 1/x)Subtract the term 'Integral(dx, 1/x)' from both sides to get:
0 = 1What is wrong with this reasoning?