1. ## Integration Problem!!

Hi,

I've been working on the following problem- the question is to integrate the following

dx/2xlog^18x.

I have used substitution letting u= log x and therefore du=dx/x. When I integrate I get 1/2[u^-17/-17 + C].Subbing back in for u this gives me 1/2[log^-17x/-17 + C].

We are asked to verify our answer by differentiating and seeing if we get the original function. However, when I differentiate I get 1/2[log^-18x] = 1/2log^18x. As you can see I am missing an x in the denominator.

I would appreciate some help please!! Keep going over it but dont know where I'm going wrong. Thanks

2. ## Re: Integration Problem!!

Originally Posted by orlacoon
when I differentiate... missing an x in the denominator.
Not if you apply the chain rule for differentiation - the working backwards through which was the point of the sub.

Would love to post a pic, have to dash - maybe later. Basically, the inner function is log x, and the chain rule tells you to multiply your derivative by the derivative of log x... voila!

3. ## Re: Integration Problem!!

Thanks a million! Seems so simple now!