Let u^2 = x
2u du = dx
and now the integral becomes
∫ 2u/(u+u^4) du = 2∫du/(1+u^3) = 2∫du/((u+1)(u^2-u+1)
= 2/3 ∫(1/(u+1) - (u-2)/(u^2-u+1)) du
= 2/3 ∫ 1/(u+1) - (1/2)(2u-1)/(u^2-u+1) + (3/2)/(u^2-u+1) du
= 2/3 ∫ 1/(u+1) - (1/2)(2u-1)/(u^2-u+1) + (3/2)/((u-1/2)^2 + 3/4) du
Now you can see how to do each of those, using log and arctan ... right?
check my math on all those fractions
Show that the following integral is convergent,
Integral, it goes from 0 to infinity dx/(sqrt(x) + x^2)
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