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Circuit Training – Integrals of “Rational” Expressions Name ______________________________ Directions: Begin in cell #1. Show the work necessary to evaluate the indefinite integral. Search for your answer. Continue in this manner until you complete the circuit. No technology needed. # _____1_____ Answer: −2 ln 𝑥 + 1 + 3 ln 𝑥 + 2 + 𝐶
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𝑑𝑥 # _________ Answer: !!!
!!!" ! !! !!!
!!!!!!!𝑑𝑥
# _________ Answer: tan!! 𝑥 + 1 + 𝐶
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𝑑𝑥 # _________ Answer: ln 𝑥 + 1 + 𝐶
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𝑑𝑥 # _________ Answer: !! !" !!!! !!
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𝑑𝑥 # _________ Answer: 𝑥 − !
!+ 𝐶
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𝑑𝑥 © Virge Cornelius 2019
# _________ Answer: !! !" !!!! !! !
!!!𝑑𝑥
# _________ Answer: ln 𝑥 − 4 + 𝐶
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!!!!𝑑𝑥
# _________ Answer: !
!𝑥 + 1 ! − 2 𝑥 + 1+ 𝐶
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𝑑𝑥 # _________ Answer: arctan 𝑥 + 𝐶 !!!!!𝑑𝑥
# _________ Answer:
!! tan!! 𝑥! + 𝐶
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𝑑𝑥 # _________ Answer: !
!𝑥! + 2 𝑥 + 𝐶
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𝑑𝑥 © Virge Cornelius 2019
# _________ Answer: !! !"#!! !! ! ! !
!!!!!𝑑𝑥
# _________ Answer: !
!tan!! 2𝑥 + 1 + 𝐶
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𝑑𝑥 # _________ Answer: !! !"#$%& !! ! ! !!!!!!!
𝑑𝑥 # _________ Answer: !!
!(!!!!)+ 𝐶
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𝑑𝑥 # _________ Answer: − !
! 1− 4𝑥! + 𝐶
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𝑑𝑥 © Virge Cornelius 2019
# _________ Answer: !!ln !!!
!!!+ 𝐶
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𝑑𝑥 # _________ Answer: 𝑥 − ln 𝑥 + 1 + 𝐶
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𝑑𝑥 # _________ Answer: !!!!! ! ! !!!!!!
𝑑𝑥 # _________ Answer: !
!𝑥! + 2𝑥 + 2 ln 𝑥 + 1 + 𝐶
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𝑑𝑥 # _________ Answer: 2𝑥 − 3 ln 𝑥 + 2 + 𝐶 !!!!𝑑𝑥
© Virge Cornelius 2019
