Mohon bantuannya kakk

Mohon bantuannya kakk

Jawab:

Penjelasan dengan langkah-langkah:

Metode 1 :

$displaystyle int frac{2t^2-t-20}{t^2+t-6} ; dt = intdfrac{dbinom{2t^2+12t+18}{-12t-18-t-20}}{(t+3)(t-2)}; dt\int frac{2t^2-t-20}{t^2+t-6} ; dt = intdfrac{2(t+3)^2-13t-38}{(t+3)(t-2)}; dt\\int frac{2t^2-t-20}{t^2+t-6} ; dt = int left(dfrac{2(t+3)^2-13(t+3)+1}{(t+3)(t-2)}right); dt\int frac{2t^2-t-20}{t^2+t-6} ; dt = int left(dfrac{2(t-2+5)}{t-2} - 13+dfrac{1}{(t+3)(t-2)}right); dt$

$displaystyle int frac{2t^2-t-20}{t^2+t-6} ; dt = int left(dfrac{10}{t-2} +dfrac{t+3-t+2 - 4}{(t+3)(t-2)}right); dt - 11t\ int frac{2t^2-t-20}{t^2+t-6} ; dt = int left(dfrac{11}{5(t-2)} -dfrac{1}{5(t+3)}right); dt - 11t\\int frac{2t^2-t-20}{t^2+t-6} ; dt =dfrac{lnleft| dfrac{(t-2)^{11}}{t+3} right|}{5}- 11t+C\\boxed{boxed{int frac{2t^2-t-20}{t^2+t-6} ; dt = lnleft| sqrt[5]{dfrac{(t-2)^{11}}{t+3} } right|-11t+C}}$