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.

OC
Answered by Olivia C. Maths tutor

5729 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is Mathematical Induction?


Prove the change of base formula for logarithms. That is, prove that log_a (x) = log_b (x) / log_b (a).


integrate (4x^3 +3)(x^4 +3x +16)^2 dx


Why do I need to add the + C when finding an indefinite integral?


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning