- #1

- 51

- 0

Will Binomial expansion work?

Please give me some clue.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter mdnazmulh
- Start date

- #1

- 51

- 0

Will Binomial expansion work?

Please give me some clue.

- #2

- 586

- 1

- #3

- 51

- 0

Can you plz help me how can I solve above integral?

- #4

- 586

- 1

Well, the easiest way is probably to look it up it an table of integrals

Wikipedia states that

where s is the square root of x^2-a^2.....taking m=0, n=1 should help you.

maybe that is not the bsst way to go.

I rather suggest the following; use simple substitutions to reduce the integrand to

[tex]

(x^2+1)^{-3/2}

[/tex]

then use [itex]x=\sinh(z)[/itex] to obtain

[tex]

\int_{\mathbb{R}}{\frac{dz}{\cosh(z)^2}}

[/tex]

Once you have that, we can think about the next steps

Wikipedia states that

where s is the square root of x^2-a^2.....taking m=0, n=1 should help you.

maybe that is not the bsst way to go.

I rather suggest the following; use simple substitutions to reduce the integrand to

[tex]

(x^2+1)^{-3/2}

[/tex]

then use [itex]x=\sinh(z)[/itex] to obtain

[tex]

\int_{\mathbb{R}}{\frac{dz}{\cosh(z)^2}}

[/tex]

Once you have that, we can think about the next steps

Last edited:

- #5

- 51

- 0

I found quite similar integral in no. 40 in the table's list ( sorry it's quite difficult to write that integral along with its result here) . But How can I obtain that result?

- #6

- 586

- 1

[tex]

\int_{\mathbb{R}}{\frac{dz}{\cosh(z)^2}}

[/tex]

?

- #7

- 51

- 0

z^2- 8 z + 36 = u

2z -8 =du/dz

but dz = du/ (2z-8)

see there's a 'z' in the denominator on right hand side. So, letting z^2- 8 z + 36 = u won't work. What I can do now?

- #8

- 586

- 1

thus your first substitution would be

y = x-4.

then

w = y/sqrt(20)

and finally

sinh(z)= w.

- #9

- 51

- 0

yeah. Thank u so much . Now I think I can manage the rest of the things.

Share: