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Find the integral

renyikouniao

Member
Jun 1, 2013
41
Question:Integrate x/((4-x^4)^0.5)

I tried to solve this using Integral1/((1-x^2)^0.5)=sin^-1(x)
But it didn't work out since theres x at the top.

And then I tried using u=4-x^4 ,It didn't work out neither
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Use the subtitution \(\displaystyle u = x^2\)
 

renyikouniao

Member
Jun 1, 2013
41

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667

renyikouniao

Member
Jun 1, 2013
41
Doesn't that look familiar ? , just a little modification .
If you mean integral (1/((a^2-x^2)^0.5)=sin^-1(x/a)+c?Our professor doesn't want us ues this.Do you have any other method?
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667

renyikouniao

Member
Jun 1, 2013
41

renyikouniao

Member
Jun 1, 2013
41

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Do you have any suggestions on how to solve this?:confused:
\(\displaystyle \frac{1}{\sqrt{4-x^2}} = \frac{1}{2\sqrt{1-\left(\frac{x}{2}\right)^2}}\)

Now you can use the substitution \(\displaystyle u = \frac{x}{2}\)
 

renyikouniao

Member
Jun 1, 2013
41
\(\displaystyle \frac{1}{\sqrt{4-x^2}} = \frac{1}{2\sqrt{1-\left(\frac{x}{2}\right)^2}}\)

Now you can use the substitution \(\displaystyle u = \frac{x}{2}\)
Thank you;),but what about the x on the top,should I rewrite x=2u?But if I do so,I can't use integral 1/((1-x^2)^0.5) right?

Integrate x/((4-x^4)^0.5)
 

ZaidAlyafey

Well-known member
MHB Math Helper
Jan 17, 2013
1,667
Then the integral becomes 1/(2(4-u^2)^0.5) du?How to simplify this?
You already arrive to this part . you can do the little trick I provided .

otherwise

\(\displaystyle \frac{x}{\sqrt{4-x^4}} = \frac{x}{2 \sqrt{1-\left( \frac{x^2}{2} \right)^2}}\)

you can know make the subtitution \(\displaystyle u = \frac{x^2}{2}\)
 

renyikouniao

Member
Jun 1, 2013
41
You already arrive to this part . you can do the little trick I provided .

otherwise

\(\displaystyle \frac{x}{\sqrt{4-x^4}} = \frac{x}{2 \sqrt{1-\left( \frac{x^2}{2} \right)^2}}\)

you can know make the subtitution \(\displaystyle u = \frac{x^2}{2}\)
Thank you very much for you patients(flower)(flower)(flower)