Exercise · ZW-INDEFINITE-INTEGRAL-009 · ★★☆ Intermediate
Compute \(\int 2x\,e^{x^{2}}\,dx\).
Choose one option.
Show answer
- D. \(e^{x^{2}}+C\)
Explanation
With \(u=x^{2}\), we have \(du=2x\,dx\), so the integral is \(\int e^{u}\,du=e^{u}+C\).
Review the concept: Indefinite integral
The indefinite integral of \(f\) is the family of all its antiderivatives, written with a constant of integration \(C\).
\[\int x^{n}\,dx=\frac{x^{n+1}}{n+1}+C\quad(n\neq-1)\]
More practice problems: indefinite integral
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- ZW-INDEFINITE-INTEGRAL-005 What is ∫ cos x dx?
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- ZW-INDEFINITE-INTEGRAL-007 Compute ∫ e^2x dx.
- ZW-INDEFINITE-INTEGRAL-008 Compute ∫ (x^2+1)/(x) dx for x>0.