Well, a and b both give you the same answer. You're just using two techniques to solve for it.
Honestly, though, i've never done a problem like this before. What does your answer say?
Wow, i'm kinda off with what I got. xp
Hi, I think this should be fairly basic for you guys(/girls?).
By using the substitution (a) u=2x+7 and (b) u^2=2x+7 find the indefinite integral of x(2x+7)^1/2 dx. I'm fine with the process of finding (a) but there is no examples in the text book for finding (b), so I don't understand what it wants me to do? There is only a single answer in the back of the book, not an answer for (a) and (b). What the? And thank you in advance for your time.
Wow, i'm really off. =p You mean, 3/2 for that last power, though, hopefully? Otherwise i'm completely lost.
Ok, so let u = 2x + 7, now replace all your x values with u.
... ...
So that your new equation looks like this:
Now go ahead and multiply everything out:
So that's
Now we simply raise the power and divide by that power.
thanks derfleurer. I get it now. I had know idea I could rearrange u=2x+7 to get x and then sub that in to the original equation. I was that x that was stuffing me up. One thing, when you said u and u^2 would give me the same answer, I don't understand why? Will there some times be questions when I will need to recognise I need to sub u^2 instead of just u?
Sometimes one substitution is easier than another, yes. But again, they still both work. So it's not like you have to recognize one over the other.
Look at the original equation:
With u = 2x + 7, our substituted formula was
However, with , we have to rearrange the formula according to new rules. So, if , what is u? u is .
So in this case, we replace with just . We replace x with . And our du = (i'll let you figure out what dx is =p)