# Standard Problems in Calculus(Part 2)

Calculus Level 5

We have a continous and differentiblel curve $$y=f(x)$$ passing through $$(1,0)$$

Let the slope of the tangent at the point $$(x,f(x))$$ be $${m}_{1}$$ and the slope of the line joining the point and the origin be $${m}_{2}$$.

Now, the ratio of $$\left| log({ m }_{ 1 }+{ m }_{ 2 }) \right|$$ and $$\left| log(x) \right|$$ is $$2:1$$

There are exactly two functions satisfying this property let them be $${f}_{1}(x)$$ and $${f}_{2}(x)$$

Find $$\int _{ 1 }^{ e }{ ({ f }_{ 1 }(x)+{ f }_{ 2 }(x))dx }$$

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