How do you find the integral of (2+5x)e^3x ?
If we were to expand the brackets for this question we might be able to get to an answer however there is a much simpler way of solving the problem. As this question is made up of two expressions of x multiplied together we can use integration by parts and say that u = 2+5x and v' = e^3x. By following the formula for integration by parts we get that u' = 5 and v = 1/3e^3x. Now that we have all this information we can substitute it into the formula, which leaves us with a much simpler integral to find for 5/3e^3x. And so by integrating this following the usual method, we get the answer which is 1/3(2+5x)e^3x - 5/9e^3x + c where c is a constant.
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