Integrating....

[selter01]

Integrate 5x/[ SQRT (x^4+1)]

I did
INT 5x/ SQRT( [x^2]^2 + 1. u = x^2, dx = du/2x

so (5/2)INT 1/SQRT ( u^2 + 1) du

and I don't know how to proceed from there ._.

[yyat]

Hint: What is the derivative of arsinh(x)?

[Gib Z]

Or if you aren't familiar with hyperbolic trig functions, try u= sec y.