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lV Tarea de cálculo ll por Lic. Andy Palmaejercicios 7.1 del 1 al 24 integración por partes

formula = − 1. = ∗13 − 13 =3−13 =13 −13∗13 + =− +

2. 2 = ∗12 2 −12 2 =12 2 −12 sin2 =12 2 −12∗−12 2 + …= + + ó ++

3. = − sec = −| +|+

4. 3=3 3− 3 3 = 3 3−1 33 3+ =− +

5. 5 = −1 = − +

6. sin = sin−√1−

= sin− − 1− + = + −+

= =

= =13

= = 2 = =12 2

= = tanx= =

= =3 = =3 3

3 3=3ln3+

= = =1 =

=sin = =1√1− =

= = 2

= =−12cos2

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7. ( ) = ( ) ( )=( )2+1+ =( )+ 8. = − = −| |+

9. tan =tan − =tan − +1− …=12 tan −12 +12tan + = − + − + 10. ln( +1) = ln( +1)− ∗2+1 = ln( +1)−2 11+1 =⋯

+ − + + 11. ( +1) =−+1− −1+1( + ) =− +1+ =− ++ +

12. sin3 =−13 cos 3 − −213 cos 3 =⋯→=−13 cos 3 +23 cos 3 =⋯→=−13 cos 3 +23 ∗13 3 −13 3 =−13cos3 +29 3 −29 −13cos3 =⋯ −13cos3 +29 3 −29 −13 cos3 + =− + + +

13. ( ) = = − =12 −12 + = − +

14. ( ) = ln( ) =−

=− (ln )−12 =− ln + = − ln + + =− ( )+ + 15. cos =sin −sin =sin −(−cos +cos )= (sin +cos)+2 = + +

= =se =1 =

=tan = =11+ =12

=ln( +1) = =2+1 =

= =1( +1) =( + ) =−1+1

= = 3 →= ==2 =−13 3 →= 13

ln=x y=e du=dxu=sinx dv du=cosx v

t=cosdt=−sinu=ln dvdu=

12dt v=−u=e dv=cos = =s

u=e dv=sin = =c

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16. =( ) = 2= 12 =12 − …→

=12 − + =12 −( +)+ =12 − +1+ …→ = − + +

17. √1−=− 1−+ 2 1− =− −− − +

18.sin2x = 2 −1 − −12 2 =− − 2cos2 −1 2 … =21cos2 − −1 2 =2(cos2 −1 − −1 (−2sin2 ) −1sin2 … =2(−2sin2 −1cos2 )−1sin2 =−22sin2 −1sin2 −2cos2 …=−2(21sin2 )−1 2 − 2cos2 = −41sin2 −1 2 − 2cos2 … =−41sin2 −1 2 −2cos2 + =−15 (sin2 −2cos2 )+ =15 sin2 −25 cos2 +

19. sinh =cosh −2 ∗cosh =cosh −2 ℎ =…→cosh −2( sinh )−2 sinh =cosh −2 sinh +2cosh

20. ( ) =√ ( )√ =( )( )√ =( − ) =− +( −3)+ =√ 1−(1−−3)+ =√ − ( +)+

. √ √ = = + + = +( +)+ √ √ +√ +( +)+

. = − ∗−− = −−√

=⋯→−√ = − = − = ..→−∗ + = −+ = −+ = − − +

z=x =2 u= = =

u=z = =

u=x =√ = 2 =−

u=sin2 =2cos2 u=cos2

=−2sin2

u=x =sinh =2x = u=x =cosh

=1 =sinh

u=1−e =−e =1−

t=√ =√ √ = √ √ =2cot dtu=cot =√ √ = =t

u=cos2 =

=1∗ =

h=1−4x2 ℎ=8

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. √ =√ = = − = + √ √ +√ +c

. √ = =√ == + − ++ =+ − = + − + =( +) √ −√ +

x=t =2 Sustitución

u=2t=2 =cos v=sin

u=tan=1+ =2 v=z+1

z=√ = =2 v=sin

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lV Tarea de cálculo ll por Lic. Andy Palmaejercicios 7.2 del 7 al 26 integración por partes

formula = − . =( + ) = + +

. = [ (− )+ ] =(− + ) =( −

− +

. =(− + ) = − +

. = ( + ) = + + = + +

. = − = − +

. ( ) = ( )( )= = − = − + =− +

. = = − =− −+ =− − +

. = − =− − +

. =− =( )− = −−| |+

. = = − = ( ) − = − − = − + +

. = −= − = − + = − + − = − + +

U=e x du= e x

U=2x 2 du= 4x dx

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. =− + =− −( + )+

. = + = + +

. = = − = −. =− − = − − −− =− − (− )+ = −+ +| |+

21. tan( ) = =→ = = tan = tan(sec−1) = tan − (sec−1) =1

3tan ̂ 3 u−tan u+u+c=1/3tan ̂ 3(e^(e^x)+e^x+c

22. sec = =1 = sec = secsec = (tan+1) (tan ) =13tan +tan + + =13tan(ln )+tan(ln )+

23. tan = tan(tan+1)sec = (tan+tan)sec =19tan +17tan +

24. tan = tansec(tan sec ) = (sec+1)^2 (sec tan =sec → =(sec tan ) =tan sec =( −1) =( −2+ ) …→ 17 −25 +13 + =17sec −25sec +13sec +

25. cot3 csc3 = cot3( 3 +1) 3 =12 (cot3 +cot3 )(3csc3 ) = (sec5 +csc5 ) (sec5 +2sec5 csc5 +csc5 ) = (sec5 +4csc10 +csc5 )15tan5 +410 ln |tan5 |−15cot5 +

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lV Tarea de cálculo ll por Lic. Andy Palmaejercicios 7.3 integración por partes

formula = − 1. √4−= ( =2sin∅ 00 −12 ≤∅