The incorrect solution is to simply take the square root of e^(9x) and integrate it, resulting in an answer of 1/18 * e^(9x/2) + C.
This solution does not take into account the chain rule, which is necessary when integrating exponential functions. The correct solution requires substitution and integration by parts.
The correct solution involves substituting u = e^(9x) and du = 9e^(9x)dx, which allows us to rewrite the integral as ∫sqrt(u)/9 du. We can then use integration by parts to solve for the integral and substitute back in u to get the final answer.
Yes, another common mistake is forgetting to add the constant of integration (C) at the end of the solution. This constant is necessary because when we take the derivative of a constant, it is equal to 0.
It is important to remember the rules of integration, such as the chain rule and integration by parts, and to always double check your work to make sure you have not made any errors. Practice and familiarity with these rules will also help to avoid making mistakes in the future.