Teaching DSSSB TGT Mock Test 2025 Mathematics Integral Calculus Definite Integrals

What is \(\rm \displaystyle\int_0^1 \frac{{{e^{{{\tan }^{ - 1}}x}}dx}}{{1 + {x^2}}}\) equal to ?

1
\({e^{\frac{\pi }{4}}} - 1\)
2
\({e^{\frac{\pi }{4}}} + 1\)
3
 \({e^{\frac{\pi }{2}}} + 1\)
4
e
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