Ejercicio 12 fundamentos matematicos

[pic 1]

Nombre: Alan Jaziel Ruiz

Matricula: 2894490

Ejercicio 12

Fundamentos matemáticos

Resuelve la integral     [pic 2]

U= ln(x)      dv= 1/x dx

Deriva U

Du= x2 dx       v= ∫ x2 – dx = x3/3

X3/3 lnx - ∫ x3/3 * 1/x dx

X3/3 lnx - ∫ x*x*x/3*x dx

X3/3 lnx - ∫x2/3 dx =

= x3/3 ln – x3/(3)(3) + U 

Resuelve la integral   [pic 3]

U= x        Dv= [e] x

Deriva U

Du= e 3x dx    V= e3/3

= Xe 3x - ∫ e 3x / 3 dx

= Xe 3x  * 1/3 (e 3x / 3) + C

= Xe 3x  / 3 – 1/9 e 3x + C

Resuelve la integral ∫ x2cos(x)dx

U= x2   Dv= Cos (x) dx

Du= 2x      V= Sin (x) dx

= x2 * Sin (x) - ∫ Sin (x) * 2x dx = x2 * Sin (x) – 2 ∫ Sin (x) dx

= X2 * Sin (X) – 2 (x * (-Cos (x)) - ∫-Cos (x) dx = X2 Sin (x) -2 (-x*cos (x) + ∫ cos (x) dx

= x2*sin(x) + 2x cos (x) – 2 Sin (x) + C

Resuelve la integral X Raiz X+2 dx

U= x+2

Du = 1 Dx

∫(U-2) Raiz U Du = ∫U 3/2 – 2 Raiz U Du = ∫U 3/2 du-2 = ∫U ½ Du

=∫x Raiz X + 2 dx = U 5/2 / 5/2 – 2 U 3/2 / 3/2  = 2/5 U 5/2 – 4/3 U 3/2

= 2/5 (x+2) 5/2 – 4/3 (x+2) 3/2 + C

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