1. ∫(4x2-16x+7)4 (x-2) dx
u=4x^2 - 16x + 7; du=(8x-16); o: du= 8(x+2)*dx; dx=du/[8(x+2)];
reemplazo y simplifico: ∫(u^4) (x-2) du/ [8(x+2)];
(1/8) ∫ u^4*du; integro:
(1/40) u^5 + C; devuelvo variable:
(1/40) (4x^2-16x+7)^5 + C
2. ∫s(s^3 -4) ds/√(s^5-10s^2+6);
u=s^5-10s^2+6; du=(5s^4 - 20s)ds; o: du=5s(s^3-4)ds; ds=du/[5s(s^3-4)];
reemplazo y simplifico:
∫ du/√u; o: ∫ u^(-1/2) du; integro:
2*u^(1/2) + C; o: 2√u + C; devuelvo variable:
2√(s^5-10s^2+6) + C
3. ∫√(3-2/v)dv/v2
∫√ [3 - (2/v)] dv / v^2; u=√ [3 - (2/v)]; du= {1/2√ [3 - (2/v)]} * (1/v^2)*dv;
pero como: u=√ [3 - (2/v)]; reemplazo y queda:
du= (1/2u) * (1/v^2)*dv; dv= du*2u*v^2; reemplazo y simplifico:
2* ∫ u^2*du; integro:
(2/3) u^3 + C; devuelvo variable:
(2/3) [√ [3 - (2/v)]}^3 + C; o:
(2/3) * [3 - (2/v)]^(3/2) + C