Integrate e^(2x)

To integrate e^(2x), integration by substitution can be used.

2x=u, you're left with an intergrand of e^u. 

S: = integral sign

S: e^u dx. In this case we are still integrating the intergrand in terms of x so we much switch it so that we are integrating in terms of u, we do this by differentiating u=2x. this equals du/dx=2. Through simple re-arrangement we get dx= 0.5du. Now we cna sub this into our new integral.

0.5S: e^u du. e to any power, when integrated is just e to that same power so we get 0.5e^u. 

Now all that's left is to sub back in the value of u which then turns our answer to 0.5e^(2x)

EJ
Answered by Emil John M. Maths tutor

32340 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

How can I determine the characteristics of a curve on an x-y set of axis (eg. points of intersection, stationary points, area under graph)?


Prove that (1-cos2x)/sin(2x) = tan(x) where x ≠ nπ/2


Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.


Differentiate z = e^(3y^2+5) with respect to y. (Hint: use chain rule.)


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences