Approaching Infinity: Solving Improper Integrals with Calc II Techniques

[demersal]

Homework Statement

$$\int\frac{x}{(x^2+2)(x^2+2)}$$ dx from 0 to infinity

Homework Equations

Improper integrals

The Attempt at a Solution

Lim$$_{t->\infty}$$ $$\int$$$$\frac{t}{0}$$ ($$\frac{x}{(x^2+2)(x^2+2)}$$)

I tried integrating this by parts and also by partial fractions but neither seemed to lend itself nicely to the problem. (Choosing dv = (x^2+2)^(-2) made finding v ugly and based on the rules for choosing u shouldn't I choose x to be u?) And partial fractions didn't seem to work either. Any suggestions?

 

[Dick]

That's a pretty ugly tex post but if you mean the integral of x*dx/(x^2+2) try u=x^2+2.

 

[demersal]

I am still trying to play with the formatting, sorry, I will write it out in words in the mean time: the integral of x over (x^2+2)^2 dx.

But, yes, it seems like that simple u-substitution will work! Thank you ... I feel so silly for overcomplicating the problem!