S07 s1 - Ejercicios_resolver_Integrales

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Integrales
∫( f (x )± g (x ))dx=∫ f (x )dx ±∫g (x )dx ∫ x ndx=
xn+1
n+1
+c
∫
1
x
dx=lnx+c ∫ cos x dx=senx+c
∫ sen x dx=−cosx+c ∫ ex dx=ex+c
∫ f (x ) g ´ (x )dx=∫u (x ) v ´ ( x) dx=u ( x )v ( x )−∫u ´ ( x ) . v ( x )dx
u (x )=f (x )→u´ ( x )=f ´ (x) v´ (x )=g ( x)→v (x )=∫ g (x )dx
Aplicaciones
Resuelva lo siguiente:
1. ∫ cos ⁡(2 x )sen3(2 x )dx
2. ∫ xsenxdx considere u=x ,dv=senxdx
3. ∫ x e2x dx considere u=x ,dv=e2x dx
4. ∫(x2+x−2)ex dx
5. ∫ xcos ( x )dx
6. ∫ tan (3 x ) dx
7. ∫ xcos 4 xdx considere u=x ,dv=cos 4 xdx
8. ∫ tan−1dx considere u=tan−1 ,dv=dx
9. ∫ e3x sen(e3x+5)dx
10. ∫ sen(lnx )dx