What is the integral of limits 1 to 2 of function 1/x(1+logx)2 - Maths - Application of Integrals

Question

What is the integral of limits 1 to 2 of function
1/x(1+logx)2

Varun.Rawat · Accepted Answer

Let I = ∫12 dxx1 + log x2put 1 + log x = t⇒1x dx = dtas, x→1, t→1as x→2, t→1 + log 2Now I = ∫11+log2 dtt2 = -1t11+log2 = -11 + log 2 - 1=1 - 11+log 2=1 + log 2 - 11 + log 2=log 21 + log 2