Integration question (1 Viewer)

[UnrealAnchovies]

If you have the Terry Lee, it's question 1(p) in Review Exercise 4.9.

But for those who don't, this is the question:

Integrate: sq.root (1 + 4x) / (1-4x) dx (the whole fraction is under a sq.root).

It's probably something really straightforward that I can't see...

Thanks in advance.

 

[Shadowdude]

Is it... this?



If so, I'll get my notepad out and start figuring it out.

 

[iSplicer]

Is it... this?



If so, I'll get my notepad out and start figuring it out.

Rationalise the numerator and substitute it out.

 

[UnrealAnchovies]

Yeah it is Shadowdude.

And I'll give that a go, thanks iSplicer.

Edit: It came out with iSplicers advice. Thanks!

 

[Drongoski]

Is it... this?



If so, I'll get my notepad out and start figuring it out.

integral = int sqrt[(1+4x)(1+4x)/(1-4x)(1+4x)] dx = int (1+4x)/sqrt(1-(4x)^2) dx

= int 1/sqrt(1 - (4x)^2) dx + int (1 - 16x^2)^(-0.5)4x dx

= 1/4 sin^-1 (4x) - 1/8 int (1 - 16x^2)^(-0.5)d(1-16x^2)

= 1/4 sin^-1(4x) - 1/4 sqrt (1- 16x^2) + C







Edit: I have been struggling to get my TeX version right ! Ha Ha!