Worksheet: Integrals Resulting in Logarithmic Functions

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

Q1:

Determine 𝑥+7𝑥+21𝑥5𝑥d.

  • A 3 | | 𝑥 + 2 1 𝑥 5 | | + l n C
  • B l n C | | 𝑥 + 2 1 𝑥 5 | | +
  • C 1 2 | | 𝑥 + 2 1 𝑥 5 | | + l n C
  • D 1 3 | | 𝑥 + 2 1 𝑥 5 | | + l n C

Q2:

Determine 8𝑒𝑥+𝑒5𝑒𝑥𝑥d.

  • A 8 1 5 𝑒 + 1 5 | 𝑥 | + l n C
  • B 8 𝑒 5 + 1 5 | 𝑥 | + l n C
  • C 8 𝑒 5 + 1 5 | 𝑥 | + l n C
  • D 8 𝑒 5 + 1 5 | 𝑥 | + l n C

Q3:

Determine 1610𝑥𝑥𝑥lnd by using the substitution method.

  • A 8 ( 1 0 𝑥 ) + l n C
  • B l n C 1 0 𝑥 +
  • C 1 0 ( 1 0 𝑥 ) + l n C
  • D 1 1 0 ( 1 0 𝑥 ) + l n C
  • E 1 8 ( 1 0 𝑥 ) + l n C

Q4:

Using the substitution method, determine (10𝑥)𝑥𝑥lnd.

  • A 1 1 0 ( 1 0 𝑥 ) + l n C
  • B 9 ( 1 0 𝑥 ) + l n C
  • C 1 1 0 ( 1 0 𝑥 ) + l n C
  • D 1 9 ( 1 0 𝑥 ) + l n C
  • E 1 0 ( 1 0 𝑥 ) + l n C

Q5:

Determine 5𝑒𝑥+5𝑥6𝑥lnd.

  • A 5 𝑒 4 | 𝑥 | + 5 𝑥 3 6 + l n l n C
  • B 5 𝑒 | 𝑥 | + 5 𝑥 3 6 + l n l n C
  • C 5 𝑒 | 𝑥 | + 5 𝑥 6 + l n l n C
  • D 5 𝑒 | 𝑥 | + 5 𝑥 2 6 + l n l n C

Q6:

Determine 37𝑥𝑥𝑥lnd.

  • A l n l n C | 𝑥 | +
  • B 3 7 𝑥 + l n C
  • C 3 7 𝑥 | 𝑥 | + l n l n C
  • D 3 7 | 𝑥 | + l n l n C

Q7:

Determine (9𝑥)7𝑥𝑥logd.

  • A 3 9 𝑥 7 1 0 + l n l n C
  • B l n l n C 9 𝑥 2 1 1 0 +
  • C 1 2 1 9 𝑥 + l n C
  • D 3 7 9 𝑥 + l n C

Q8:

Determine 𝑥163𝑥12𝑥𝑥d.

  • A 4 3 | 𝑥 | + l n C
  • B 4 3 | 𝑥 | + l n C
  • C 𝑥 3 + 4 3 | 𝑥 | + l n C
  • D 𝑥 3 4 3 | 𝑥 | + l n C

Q9:

Determine 54𝑥𝑥𝑥lnd by using the substitution method.

  • A 5 2 ( 4 𝑥 ) + l n C
  • B l n C 4 𝑥 +
  • C 4 ( 4 𝑥 ) + l n C
  • D 1 4 ( 4 𝑥 ) + l n C
  • E 2 5 ( 4 𝑥 ) + l n C

Q10:

Determine 𝑒𝑥+7𝑥4𝑥lnd.

  • A 𝑒 2 | 𝑥 | + 7 𝑥 3 4 + l n l n C
  • B 𝑒 | 𝑥 | + 7 𝑥 3 4 + l n l n C
  • C 𝑒 | 𝑥 | + 7 𝑥 4 + l n l n C
  • D 𝑒 | 𝑥 | + 7 𝑥 2 4 + l n l n C

Q11:

Find 2𝑥9+2𝑥𝑥d to the nearest hundredth.

Q12:

Determine 2𝑥152𝑥+5𝑥tantand.

  • A 1 1 0 | 2 𝑥 + 2 𝑥 | + l n s i n c o s C
  • B 1 1 0 | 𝑥 + 𝑥 | + l n s i n c o s C
  • C 1 1 0 | 2 𝑥 + 2 𝑥 | + l n s i n c o s C
  • D 2 5 | 2 𝑥 + 2 𝑥 | + l n s i n c o s C

Q13:

Determine 57𝑥𝑥secd.

  • A 5 | 7 𝑥 + 7 𝑥 | + l n t a n s e c C
  • B 5 7 | 7 𝑥 + 7 𝑥 | + l n t a n s e c C
  • C 5 7 7 𝑥 7 𝑥 + s e c t a n C
  • D 3 5 ( 7 𝑥 7 𝑥 ) + l n s e c t a n C

Q14:

Determine 9𝑥𝑥5𝑥19𝑥tansecsecd.

  • A 9 5 | 5 𝑥 1 9 | + l n s e c C
  • B 9 | 5 𝑥 1 9 | + l n s e c C
  • C 9 5 | 𝑥 1 9 | + l n s e c C
  • D 9 5 | 5 𝑥 1 9 | + l n s e c C

Q15:

Determine 27𝑥𝑥cscd.

  • A 2 7 | 7 𝑥 + 7 𝑥 | + l n c o t c s c C
  • B 2 7 | 7 𝑥 + 7 𝑥 | + l n c o t c s c C
  • C 2 7 | 7 𝑥 7 𝑥 | + l n c o t c s c C
  • D 2 7 | 7 𝑥 7 𝑥 | + l n c o t c s c C

Q16:

Determine 73𝑥53𝑥𝑥sectand.

  • A 7 1 5 | 3 𝑥 | + l n s e c C
  • B 7 1 5 | 3 𝑥 | + l n t a n C
  • C 7 1 5 | | 3 𝑥 | | + l n s e c C
  • D 7 1 5 | 3 𝑥 | + l n t a n C

Q17:

Determine 418𝑥+89𝑥9𝑥+29𝑥+5𝑥sincossinsind.

  • A 4 9 | 9 𝑥 + 2 9 𝑥 + 5 | + l n s i n s i n C
  • B 4 9 | 9 𝑥 + 2 9 𝑥 + 5 | + l n s i n s i n C
  • C 4 9 | 1 8 𝑥 + 2 9 𝑥 | + l n s i n c o s C
  • D 4 | 9 𝑥 + 2 9 𝑥 + 5 | + l n s i n s i n C

Q18:

Determine 4+5𝑥4𝑥+5(8𝑥)𝑥tanlnsecd.

  • A l n l n s e c C | 4 𝑥 + 5 ( 8 𝑥 ) | +
  • B l n t a n C | 4 + 5 𝑥 | +
  • C | 4 𝑥 + 5 ( 8 𝑥 ) | + l n l n s e c C
  • D 1 | 4 𝑥 + 5 ( 8 𝑥 ) | + l n l n s e c C

Q19:

Determine 84𝑥24𝑥5𝑥cossind.

  • A 1 | 4 𝑥 | + l n c o s C
  • B 1 | 2 4 𝑥 5 | + l n s i n C
  • C | 2 4 𝑥 5 | + l n s i n C
  • D | 4 𝑥 | + l n c o s C

Q20:

Determine 2𝑥7𝑥+1𝑥d.

  • A 2 𝑥 ( 7 𝑥 + 1 ) + C
  • B 1 1 4 | 7 𝑥 + 1 | + l n C
  • C 1 7 | 7 𝑥 + 1 | + l n C
  • D 2 | 7 𝑥 + 1 | + l n C

Q21:

Determine 3𝑥8𝑥𝑥lnd.

  • A 3 | 𝑥 | + l n C
  • B 3 8 | 8 𝑥 | + l n l n C
  • C 3 | 8 𝑥 | + l n l n C
  • D 3 8 | 𝑥 | + l n C

Q22:

Determine 2𝑥5𝑥13𝑥d.

  • A 1 5 | 5 𝑥 1 3 | + l n C
  • B 2 5 | 𝑥 | + 𝑥 1 3 + l n C
  • C 1 5 | 1 0 𝑥 | + l n C
  • D 1 5 | 5 𝑥 1 3 | + l n C

Q23:

Determine 6𝑥+83𝑥+8𝑥+3𝑥d.

  • A 3 | 𝑥 | + 𝑥 + 4 1 𝑥 1 2 8 3 𝑥 + l n C
  • B l n C | 3 𝑥 + 8 𝑥 + 3 | +
  • C 1 | 3 𝑥 + 8 𝑥 + 3 | + l n C
  • D l n C | 6 𝑥 + 8 | +

Q24:

Determine 56𝑥𝑥tand.

  • A 5 6 | 6 𝑥 | + l n c o s C
  • B 5 6 | 6 𝑥 | + l n s i n C
  • C 5 6 | 6 𝑥 | + l n s i n C
  • D 5 6 | 6 𝑥 | + l n c o s C

Q25:

Determine 73𝑥5𝑥3𝑥𝑥lnlnd.

  • A 1 4 5 | | 𝑥 | | + l n C
  • B 1 4 5 | 𝑥 | + l n C
  • C 1 4 5 | 𝑥 | + l n C
  • D 1 4 5 𝑥 | 𝑥 | + l n C

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