What would the result of integrating the equation twice be? d^2T/dx^2 + (constant)=0

Thanks =)

Note that the differential in the numerator names the function, and the differential in the denominator names the variable, thus this is equivalent to the second derivative of T(x).

T''(x) + C = 0

Integrating both sides:

∫ T''(x)dx + ∫C dx = ∫ (0) dx
T'(x) + Cx = K

Where K is another arbitrary constant obtained from the integrals. Again:

∫ T'(x) dx + ∫ Cx dx = ∫ K dx
T(x) + (1/2)Cx^2 = Kx + M

Where M is another arbitrary constant, thus we have:

T(x) = M + Kx - (1/2)Cx^2

Done!