Exercios 5.1 Leithold 1 ao 10

Exercicio 5.1 Leithold do 1 ao 10

1. ∫▒〖3x^4 〗 dx =∫▒〖3x^4 〗 dx → 3∫▒x^4 dx =3(1/5 x^5+C)=3/5 x^5+C

2. ∫▒〖2x^7 dx〗=∫▒〖2x^7 dx〗 → 2∫▒x^7 dx=2(x^8/8+C)=1/4 x^8+c

3. ∫▒〖1/x^3 〗 dx = ∫▒1/x^3 dx → ∫▒x^(-3) dx= -1/2 x^(-2)+C=-1/(2x^2 )+C

4. ∫▒3/t^5 dt = ∫▒3/t^5 dt → ∫▒〖3 t^(-5) 〗 dt → 3∫▒〖t^(-5) dt〗=3(-1/4 t^(-4) )+C=-3/4 1/t^4 =C=-3/(4t^4 )+C

5. ∫▒〖5u^(3/2) 〗 du = ∫▒〖5u^(3/2) 〗 du → 5∫▒u^(3/2+1)/(3/2+1)=5(u^(5/2)/(5/2))+C=5(2/5 u^(5/2) )+C=2u^(5/2)+ C

6. ∫▒〖10 ∛(x^2 )〗 dx = ∫▒〖10 ∛(x^2 )〗 dx → 10∫▒x^(2/3) dx=10(3/5 x^(5/3) )+C=6x^(5/3)+C

7. ∫▒2/∛x dx = ∫▒2/∛x dx → ∫▒2/x^(1/3) dx → 2∫▒x^(-1/3) dx=2(3/2 x^(2/3) )+C=3x^(2/3)+C

8. ∫▒3/∛y dx = ∫▒3/√y dx → ∫▒3/y^(1/2) dx → 3∫▒y^(-1/2) =3(2/1 y^(1/2) )+C=6y^(1/2)+C=6√y+C

9. ∫▒〖6t^2 ∛t〗 dt = ∫▒〖6t^2 ∛t〗 dt → 6∫▒t^2 t^(1/3) dt → 6∫▒t^(7/3) dt=6(3/10 t^(10/3) )+C=9/5 t^(10/3)+C

10. ∫▒〖7x^3 √x〗 dx = ∫▒〖7x^3 √x〗 dx → 7∫▒x^3 x^(1/2) dx → 7∫▒x^(7/2) dx=7(2/9 x^(9/2) )+C=14/9 x^(9/2)+C