integration (0-3) $\displaystyle 4x/((x-5)^2)$
integration (0-inf) $\displaystyle x^2/(4+x^6)$
It's not as "obvious":
$\displaystyle \int_0^3 \frac{4x}{(x-5)^2}dx$
$\displaystyle u=x-5 \rightarrow u+5=x$
$\displaystyle du=dx$
$\displaystyle \int_0^3 \frac{4(u+5)}{u^2}du$
Can probably take it from there. . .
For the second one, gosh - that one COULD look like the derivative of a trig function if we could only do some hand-waving (re: u-sub) to make it so. . .
$\displaystyle \int_0^\infty \frac{x^2}{4+x^6}dx$
Let me take $\displaystyle u$ to be $\displaystyle x^3$:
$\displaystyle u = x^3$
$\displaystyle du = 3x^2dx \Rightarrow \frac{du}{3} = x^2 dx$
And well hot damn, I have an "x-squared dx". Now replace all that and see what juicy derivative you get. From here it should be "elementary. . ." - hopefully. Assuming you know your trig derivatives.