Thanks ! - D - 3 XXXXXXXXXXIntegrate XXXXXXXXXXIntegrate 3. Integrate 4. Integrate 5.Evaluate (Show your work. No fnint.) 6. Using Trig. Substitution, Integrate 7.Integrate 8.Integrate 9. I Document...

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Answered Same DayDec 29, 2021

Answer To: Thanks ! - D - 3 XXXXXXXXXXIntegrate XXXXXXXXXXIntegrate 3. Integrate 4. Integrate 5.Evaluate (Show...

Robert answered on Dec 29 2021
132 Votes
D - 3
1. Integrate ∫


=∫


=∫


+∫


=∫ + ∫


= x + (1/2)*log|


+ c (from f
ormula of ∫


)
2. Integrate ∫√



∫√


dx = ∫ √
( )( )
( )( )
dx
=∫



=∫


- ∫



(putting 25-x2 = z2=>-2xdx=2zdz =>-xdx=zdz)
=5*


+ ∫


(using the formula for ∫


)
=5*


+ z +c
=5*


+ √ + c (since z=√ )
3.Integrate ∫






=∫


(putting sin2x +1 = z2 =>2sin x cos x dx = 2zdz =>cos x dx=

)
=∫



=log (z + √ ) + c
=log(√ + sin x) + c
4. Integrate ∫

=x∫ - ∫



=-x cos x + ∫
=-xcos x + sinx +c
=sin x – x cos x + c
5. Evaluate ∫


(Show your work. No fnint.)




– ∫


]1
2





]1
2
4ln 2-


6. Using Trig. Substitution, Integrate∫






= ∫


(putting x=2sin => dx= d )
= ∫



=



= -


7. Integrate∫



= 2x +


=

+


x+5=A(x-2) + B(x-4)
Solving by comparing coefiicients in the numerator, we get A=9/2,B=7/2...
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