## Calculus: Early Transcendentals 8th Edition

The answer is in an implicit form : $-t^{-1} + t^3/3 + C$
$du/dt = (1 + t^4)/(ut^2 + u^4t^2)$ This can be rewritten as: $du/dt = (1 + t^4)/((t^2)(u + u^4))$ Now it will be easier to separate u on one side and t on the other side: $(u + u^4) du = (1 + t^4)/(t^2) dt$ This can be simplified to : $(u + u^4) du = (t^{-2} + t^2) dt$ Now let's integrate both sides: $\int(u + u^4) du = \int(t^{-2} + t^2) dt$ $u^2/2 + u^5/5 = -t^{-1} + t^3/3 + C$