Integral of \( \displaystyle e^{2 x} \sin{\left(e^{2 x} \right)} \)

Problem 4.740 · medium

1. \[ \int e^{2 x} \sin{\left(e^{2 x} \right)}\, dx \]
   integral algebra algebra rewriteStart with the integral of the given function. Multiply and divide by 2 to prepare for substitution. Distribute the constant. Recognize the derivative of the inner function.✓ Proved
2. \[ = \frac{\int 2 e^{2 x} \sin{\left(e^{2 x} \right)}\, dx}{2} \]
   linearityPull the constant out of the integral.✓ Proved
3. \[ = - \frac{\cos{\left(e^{2 x} \right)}}{2} \]
   antiderivativeIntegrate the remaining expression using the substitution rule.✓ Proved