You could always use integration by substitution, with u = x^2, because then (1/2)du = xdx, and you just have to integrate [u(e^u)]/2 du - which you then do by parts .
Thanks- just had a look at noticed that when you rearranged your du/dx= 2x to get it to =dx, you left the x with the dx to give xdx= du/2. I'm probably being extremely thick here but how can you do that? I've finished C4 and i've never done that before ive always been taught to take everything over with the du to get dx on its own?
Thanks- just had a look at noticed that when you rearranged your du/dx= 2x to get it to =dx, you left the x with the dx to give xdx= du/2. I'm probably being extremely thick here but how can you do that? I've finished C4 and i've never done that before
It's just making it simpler to substitute in, for instance if you have dy/dx = 2x, dy = 2xdx; the differential becomes an integral, which takes you back to y = x^2 (+C).
You're allowed to manipulate it like that, for instance xdx = 1/2 du is the same as x^2/2 = u/2 (+C.. but let's ignore the constant here), which brings you back to your original integral when you multiply both sides by two. The integers are just a constant, it doesn't make much difference how you manipulate them as long as you stay thorough throughout.
It's just making it simpler to substitute in, for instance if you have dy/dx = 2x, dy = 2xdx; the differential becomes an integral, which takes you back to y = x^2 (+C).
You're allowed to manipulate it like that, for instance xdx = 1/2 du is the same as x^2/2 = u/2 (+C.. but let's ignore the constant here), which brings you back to your original integral when you multiply both sides by two. The integers are just a constant, it doesn't make much difference how you manipulate them as long as you stay thorough throughout.
Hey I done it your way and it worked, but when I done it the other way you end up doing IBP twice and I got an extra term on my answer :\... The second integration I had was x(e^(x^2))... I ended up getting for this integral 0.5e^(x^2)-(1\(4x^2))(e^(x^2) +c
Hey I done it your way and it worked, but when I done it the other way you end up doing IBP twice and I got an extra term on my answer :\... The second integration I had was x(e^(x^2))... I ended up getting for this integral 0.5e^(x^2)-(1\(4x^2))(e^(x^2) +c
The other way is more doing it all in one go in my opinion, it's the same method just done quicker. If you spot good substitutions in any question, use them straight away before attempting integration by parts - that's if the question needs it (generally you end up using just the one method).