How can i calculate the attached integral?

[hokhani]

How can i calculate the attached integral?

 

[Char. Limit]

Most people on PhysicsForums are understandably leery of opening a zip file. Maybe if you could type your integral out for us we'd be more likely to look at it.

 

[Mark44]

My thoughts exactly.

 

[jhae2.718]

It might be a decent idea to disallow executable files from being attached?

Please type out the integral or use $$\LaTeX$$ to display mathematics.

 

[hokhani]

ok
excuse me
i typed it here

∫(x^(2 ) dx)/(x^2+a)

 

[jhae2.718]

You should be able to use long division to get the function in integrable form.

 

[HallsofIvy]

Or:
$$\frac{x^2}{x^2+ a}= \frac{x^2+ a- a}{x^2+ a}= \frac{x^2+ a}{x^2+ a}-\frac{a}{x^2+ a}= 1- \frac{a}{x^2+a}$$

 

[jhae2.718]

Or:
$$\frac{x^2}{x^2+ a}= \frac{x^2+ a- a}{x^2+ a}= \frac{x^2+ a}{x^2+ a}-\frac{a}{x^2+ a}= 1- \frac{a}{x^2+a}$$

I'd never thought of that until you posted a similar expansion in the homework forums. It's really quite elegant compared to long division.

 

[hokhani]

thanks very much

 

[hokhani]

I can't calculate this integral:
∫dx/((1-x)(1+x^2))
please guid me
thanks

 

[Char. Limit]

For this one you're going to need to use partial fractions. That is find A, B, and C such that:

$$\frac{1}{(1-x)(1+x^2)} = \frac{A}{1-x} + \frac{Bx+C}{1+x^2}$$

You can multiply both sides by (1-x)(1+x^2), and then equate the coefficients of powers of x to get a system of equations that you can solve.

 

[hokhani]

Thank you Mis Char Limit
question:
how can i write equations ?

 

[jhae2.718]

how can i write equations ?

The forum has support for $\LaTeX$ typesetting. A guide is available here: https://www.physicsforums.com/showthread.php?t=386951

You can click on the $\LaTeX$ images to see the code used to produce them.

 

[Caramon]

Or:
$$\frac{x^2}{x^2+ a}= \frac{x^2+ a- a}{x^2+ a}= \frac{x^2+ a}{x^2+ a}-\frac{a}{x^2+ a}= 1- \frac{a}{x^2+a}$$

This is so beautiful!