Integration By Substitution

Question

Using substitution, ∫2x·e^(x²) dx equals

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1. **Substitution choice**: Let $u = x^2$.
2. **Differential**: $du = 2x \, dx$.
3. **Transform Integral**: Notice that the term $2x \, dx$ exists in the original problem.
   - $\int e^{x^2} (2x \, dx) = \int e^u \, du$
4. **Integrate**: $e^u + C$.
5. **Back Substitution**: Replace $u$ with $x^2$.
   - Result $= e^{x^2} + C$.

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Integration By Substitution

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