Mathematics - Definite Integration Question with Solution | TestHub

$f(x)={\int }_1^x\frac{\log t}{1+t}dt$ $F(e)=f(e)+f\left(\frac{1}{e}\right)$ $F(e)={\int }_1^e\frac{\log t}{1+t}dt+{\int }_1^{1/e}\frac{\log t}{1+t}dt$ $={\int }_1^e\frac{\log t}{1+t}+{\int }_1^e\frac{\log t}{t(1+t)}dt$ $={\int }_1^e\frac{\log t}{t}dt=\frac{1}{2}$.