The integrand simplifies to 1/(3x^3) + 1/(3x^4) + 1/x^5, so the integral of this is -1/(6x^2) - 1/(9x^3) - 1/(4x^4). Putting in the limits gives:
[-1/(6*4^2) - 1/(9*4^3) - 1/(4*4^4)] - [-1/(6*3^2) - 1/(9*3^3) - 1/(4*3^4)] = 3133/248832 ( = 0.012591)
I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.
I have one question though, for the integration I don't understand why the power decreases instead of increase. It may be something we haven't learnt yet as we are into the 3rd exercise of the integration chapter.
(Chuckles) But the power DOES increase. -2 > -3 for example. The power rule still applies even though the exponent is negative:
Int(1/x^n dx) = Int(x^{-n} dx ) = [1/(-n + 1)]*x^{-n + 1} + C
Don't think of it as "stupid." You are now more aware of this property, so your mistake had a use. It is better to ask the question than to not ask it.