Calculation of [math]\displaystyle \int\frac{1}{\left(1+x^4\right)^{\frac{1}{4}}}dx[/math]

 

My Trial : [math]\displaystyle \int\frac{1}{x\cdot \left(x^{-4}+1\right)^{\frac{1}{4}}}dx[/math]

 

Let [math]x^{-4}+1 = t^4[/math] and [math]\displaystyle \frac{1}{x^5}dx = -\frac{4t^3}{4}dt = -t^3dt[/math]

 

[math]\displaystyle [/math]

 

Now How can i solve after that

 

Help please

 

Thanks

 

 

Have you tried trigonometric substitution.

with x = tan²(t)

 

and then use

sec²(p)= (1+tan²(p))

Edited November 12, 201312 yr by studiot

Have you tried trigonometric substitution.

with x = tan²(t)

 

and then use

sec²(p)= (1+tan²(p))

 

Not sure I understand your substitution - that would give you tan(t) to the 8th power; shouldn't it be x^2=tan(t) to give denominator as (1+tan^2)^1/4

Yes you are right.

Transform it to something you can do trigonometric substitution

 

You know: LIATE