Let , where . If , find…

MATHEMATICS · Numerical · A Level · Mathematics · Integration · Integration

Problem

Let I(x)=∫x+1x(1+xex)2 dxI(x)=\int\frac{x+1}{x(1+xe^x)^2}\,dx, where x>0x>0. If lim⁡x→∞I(x)=0\lim_{x\to\infty}I(x)=0, find I(1)I(1).

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