The Monster Integral

Calculus Level 4

Here is the monster that will give you a nightmare. Compute the following integral 0π4[(1x2)ln(1+x2)+(1+x2)(1x2)ln(1x2)(1x4)(1+x2)]xexp[x21x2+1]dx \int_0^{\Large\frac{\pi}{4}}\left[\frac{(1-x^2)\ln(1+x^2)+(1+x^2)-(1-x^2)\ln(1-x^2)}{(1-x^4)(1+x^2)}\right] x\, \exp\left[\frac{x^2-1}{x^2+1}\right]\, dx

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