Evaluate:
Evaluate:
$\int \frac{e^x}{1 + e^{2x}} \, dx$
Answer
Answer
AIWritten by AI (gemini-2.5-pro) - it can contain mistakes.
Let $I = \int \frac{e^x}{1 + e^{2x}} \, dx = \int \frac{e^x}{1 + (e^x)^2} \, dx$.
Substitute $t = e^x$, then $dt = e^x \, dx$.
$I = \int \frac{dt}{1 + t^2} = \tan^{-1}(t) + C = \tan^{-1}(e^x) + C$
From ISC 2026 Mathematics Paper 1, question 4.