Integral of \( \displaystyle e^{9 x + 3} \)

Problem 4.378 · easy

1. \[ \int e^{9 x + 3}\, dx \]
   integralStart with the integral of the function.✓ Proved
2. \[ = \int e^{3} e^{9 x}\, dx \]
   algebraUse the property exp(a + b) = exp(a) * exp(b).✓ Proved
3. \[ = e^{3} \int e^{9 x}\, dx \]
   linearityFactor out the constant term exp(3).✓ Proved
4. \[ = \frac{e^{3} e^{9 x}}{9} \]
   antiderivativeIntegrate the exponential function.✓ Proved
5. \[ = \frac{e^{9 x + 3}}{9} \]
   simplifyCombine the terms back into a single exponent.✓ Proved