Question
evaluate the intergral using substitution
ingergral[(x^2-e^3x)/(x^3-e^3x)^2]dx
ingergral[(x^2-e^3x)/(x^3-e^3x)^2]dx
Answers
Reiny
By the "Just Look-at-it Theorem and Knowing your Derivatives" and knowing the derivative of ln(...)
I noticed that the derivative of the bottom would be
3(x^2 - e^3x) , which just happens to look awfully close to the top
so if y' = [(x^2-e^3x)/(x^3-e^3x)^2] then
y = (1/3)(ln(x^3 - e^3x))
I noticed that the derivative of the bottom would be
3(x^2 - e^3x) , which just happens to look awfully close to the top
so if y' = [(x^2-e^3x)/(x^3-e^3x)^2] then
y = (1/3)(ln(x^3 - e^3x))