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Lesson Worksheet: Integrals Resulting in Logarithmic Functions Mathematics • Higher Education

In this worksheet, we will practice evaluating integrals of functions in the form 𝑓′(𝑥)/𝑓(𝑥), resulting in logarithmic functions.

Q1:

Determine ο„Έ2π‘₯+1π‘₯+π‘₯βˆ’7π‘₯d.

  • AlnCο€Ήπ‘₯+π‘₯βˆ’7+
  • BlnC||π‘₯+π‘₯βˆ’7||+
  • ClnC(2π‘₯+1)+
  • DlnC|2π‘₯+1|+
  • Eο€Ήπ‘₯+π‘₯βˆ’7+C

Q2:

Determine ο„Έπ‘₯+7π‘₯+21π‘₯βˆ’5π‘₯d.

  • A3||π‘₯+21π‘₯βˆ’5||+lnC
  • BlnC||π‘₯+21π‘₯βˆ’5||+
  • C12||π‘₯+21π‘₯βˆ’5||+lnC
  • D13||π‘₯+21π‘₯βˆ’5||+lnC

Q3:

Determine ο„Έ27π‘₯+21π‘₯7π‘₯βˆ’9π‘₯π‘₯sincossincosd.

  • AlnsincosC|7π‘₯βˆ’9π‘₯|+
  • B3|7π‘₯βˆ’9π‘₯|+lnsincosC
  • C3|7π‘₯βˆ’9π‘₯|+lnsincosC
  • D3|9π‘₯+7π‘₯|+lnsincosC

Q4:

Determine ο„Έ4+5π‘₯4π‘₯+5(8π‘₯)π‘₯tanlnsecd.

  • AlnlnsecC|4π‘₯+5(8π‘₯)|+
  • BlntanC|4+5π‘₯|+
  • Cβˆ’|4π‘₯+5(8π‘₯)|+lnlnsecC
  • D1|4π‘₯+5(8π‘₯)|+lnlnsecC

Q5:

Determine ο„Έ37π‘₯π‘₯π‘₯lnd.

  • AlnlnC|π‘₯|+
  • B37π‘₯+lnC
  • C37π‘₯|π‘₯|+lnlnC
  • D37|π‘₯|+lnlnC

Q6:

Determine ο„Έβˆ’3π‘₯8π‘₯π‘₯lnd.

  • Aβˆ’3|π‘₯|+lnC
  • Bβˆ’38|8π‘₯|+lnlnC
  • Cβˆ’3|8π‘₯|+lnlnC
  • Dβˆ’38|π‘₯|+lnC

Q7:

Determine ο„Έβˆ’56π‘₯π‘₯tand.

  • A56|6π‘₯|+lncosC
  • Bβˆ’56|6π‘₯|+lnsinC
  • C56|6π‘₯|+lnsinC
  • Dβˆ’56|6π‘₯|+lncosC

Q8:

Determine ο„Έπ‘₯π‘₯cotd.

  • AlnsinC|(π‘₯)|+
  • BcotC(π‘₯)2+
  • ClncscC|(π‘₯)|+
  • DlncosC|(π‘₯)|+
  • Eβˆ’(π‘₯)+cscC

Q9:

Determine ο„Έ27π‘₯π‘₯cscd.

  • Aβˆ’27|7π‘₯+7π‘₯|+lncotcscC
  • B27|7π‘₯+7π‘₯|+lncotcscC
  • Cβˆ’27|7π‘₯βˆ’7π‘₯|+lncotcscC
  • D27|7π‘₯βˆ’7π‘₯|+lncotcscC

Q10:

Determine ο„Έ2+3𝑒1+𝑒π‘₯d.

  • AlnC|1+𝑒|+
  • B2π‘₯+|2+3𝑒|+lnC
  • C3|2+𝑒|+lnC
  • D2π‘₯+|1+𝑒|+lnC
  • ElnC|2+3𝑒|+

This lesson includes 51 additional questions and 261 additional question variations for subscribers.

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