∫(x^3dx)/(x^4+1)^3=
t=x^4+1, dt=4x^3dx, x^3dx=dt/4
= ∫dt/(4t^3)= 1/4∫t^(-3)dt=
=1/4*t^(-3+1)/(-3+1)+c=1/4*t^(-2)/(-2)+c=-0.125/t^2+c=
=-0.125/(x^4+1)^2, c є R
∫(x^3dx)/(x^4+1)^3=
t=x^4+1, dt=4x^3dx, x^3dx=dt/4
= ∫dt/(4t^3)= 1/4∫t^(-3)dt=
=1/4*t^(-3+1)/(-3+1)+c=1/4*t^(-2)/(-2)+c=-0.125/t^2+c=
=-0.125/(x^4+1)^2, c є R