Calculating indefinite integral

[Argiris]

Homework Statement

hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2)

Homework Equations

The Attempt at a Solution

tried to set x+1=u and integrate it by substitution but didnt work

 

[micromass]

Try to set u^2=x+1

 

[Ray Vickson]

Homework Statement

hey could you help me to calculate the indefinite integral of y=√x+1/x+2

Homework Equations

The Attempt at a Solution

tried to set x+1=u and integrate it by substitution but didnt work

It is not clear what your function y is. It could be y = \sqrt{x} + \frac{1}{x} + 2, or y = \sqrt{\displaystyle x + \frac{1}{x}} + 2, or
y = \sqrt{\displaystyle x + \frac{1}{x} + 2}. If you don't want to use LaTeX, you need to use brackets, so the first way I wrote above would be y = (√x) + (1/x) + 2, the second way would be y = √[x + (1/x)] + 2, and the thire way would be y = √[x + (1/x) + 2]. If I read your function using *standard* rules and priorities, it means the first way above.

RGV

 

[daveb]

So now you have ∫√u/(u+1)du. Try an additional substitution.

 

[Argiris]

It is not clear what your function y is. It could be y = \sqrt{x} + \frac{1}{x} + 2, or y = \sqrt{\displaystyle x + \frac{1}{x}} + 2, or
y = \sqrt{\displaystyle x + \frac{1}{x} + 2}. If you don't want to use LaTeX, you need to use brackets, so the first way I wrote above would be y = (√x) + (1/x) + 2, the second way would be y = √[x + (1/x)] + 2, and the thire way would be y = √[x + (1/x) + 2]. If I read your function using *standard* rules and priorities, it means the first way above.

RGV

I apologize for the missunderstanding the function is y=Sqrt[x+1]/Sqrt[x+2] i corrected it in the question to.

 

[Argiris]

Try to set u^2=x+1

well i tried it and this transformed the integral into ∫2*(u^3)/√(u^2+1)du. then i set u=tanθ and the integral is transformed into 2∫(tanθ^3)*secθdθ. and couldn't take it any further..

 

[dextercioby]

u = \sinh t seems a better substitution.

 

[NascentOxygen]

EDIT: double posting. see next post.

 

[NascentOxygen]

well i tried it and this transformed the integral into ...

I don't get that u^3.

 

[clanijos]

Indeed sinh does seem like a better option here

 

[SammyS]

Homework Statement

hey could you help me to calculate the indefinite integral of y=√(x+1)/√(x+2)

Homework Equations

The Attempt at a Solution

tried to set x+1=u and integrate it by substitution but didn't work

Similar, but slightly different than what micromass suggested.

Use the substitution: u=\sqrt{x+2}\,, then \displaystyle du=\frac{dx}{2\sqrt{x+2}}\,.

This also gives \sqrt{x+1}=\sqrt{u^2-1}\,.

 

[NascentOxygen]

A good substitution does wonders to an unrecognizable result.

Unleashing wolfram alpha on the original expression: http://www.wolframalpha.com/input/?i=integrate+sqrt%28x^2%2B1%29%2Fsqrt%28x^2%2B2%29

But make good use of an appropriate substitution and we end up with something recognizable. (Assuming I haven't blundered. )

Use the substitution: u=\sqrt{x+2}\,,

http://www.wolframalpha.com/input/?i=int+2+sqrt%28u^2-1%29