The value of ∫1e (1+x2 ln x/x+x2 ln x) d x is

Question

The value of ∫1e (1+x2 ln x/x+x2 ln x) d x is (A) e (B) ln(1+e) (C) e+In(1+e) (D) e- In (1+e)

Tardigrade Admin · Accepted Answer

I=∫1e((1/x)+1) d x-∫1e (1+ ln x/1+x ln x) d x =[ ln x+x]1e-[ ln (1+x ln x)]1e =e- ln (1+e)

Q. The value of $\int_{1}^{e} \frac{1 + x ^{2} l n x}{x + x ^{2} l n x} d x$ is