Mathematics Integral Calculus Definite Integrals

The value of \(\int_{-1}^1\left|\tan ^{-1} x\right| d x\) is:

1
\(\frac{\pi}{2}-\log _{\mathrm{e}} 2\)
2
\(\frac{\pi}{2}+\log _{\mathrm{e}} 2\)
3
\(\frac{\pi-1-\log _{\mathrm{e}} 2}{2}\)
4
\(\frac{\pi-1+\log _{\mathrm{e}} 2}{2}\)

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