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Lesson Worksheet: Integration by Substitution: Indefinite Integrals Mathematics • Higher Education

In this worksheet, we will practice using integration by substitution for indefinite integrals.

Q1:

Determine ๏„ธ8๐‘ฅ(8๐‘ฅ+9)๐‘ฅ๏Šจd by using the substitution method.

  • A124(8๐‘ฅ+9)+๏ŠฉC
  • Bโˆ’916(8๐‘ฅ+9)+๏ŠชC
  • C132(8๐‘ฅ+9)โˆ’38(8๐‘ฅ+9)+๏Šช๏ŠฉC
  • D124(8๐‘ฅ+9)โˆ’916(8๐‘ฅ+9)+๏Šช๏ŠฉC
  • E124(8๐‘ฅ+9)โˆ’916(8๐‘ฅ+9)+๏Šฉ๏ŠจC

Q2:

Determine ๏„ธ๐‘ฅ๏€น๐‘ฅ+9๏…๐‘ฅ๏Šซ๏Šฌ๏Šญd.

  • A16๏€น๐‘ฅ+9๏…+๏Šฌ๏ŠฎC
  • B148๏€น๐‘ฅ+9๏…+๏Šฌ๏ŠฎC
  • C๐‘ฅ48๏€น๐‘ฅ+9๏…+๏Šฌ๏Šฌ๏ŠฎC
  • D18๏€น๐‘ฅ+9๏…+๏Šฌ๏ŠฎC

Q3:

Determine ๏„ธ๐‘ฅโˆ’11(๐‘ฅโˆ’2)๐‘ฅ๏Šฏd.

  • Aโˆ’17(๐‘ฅโˆ’2)+1(๐‘ฅโˆ’2)+๏Šญ๏ŠฏC
  • Bโˆ’17(๐‘ฅโˆ’2)+1(๐‘ฅโˆ’2)+๏Šญ๏ŠฎC
  • Cโˆ’17(๐‘ฅโˆ’2)+98(๐‘ฅโˆ’2)+๏Šญ๏ŠฎC
  • Dโˆ’17(๐‘ฅโˆ’2)+910(๐‘ฅโˆ’2)+๏Šญ๏ŠฎC

Q4:

Determine ๏„ธ47๏€ผ7๐‘ฅ5+1๏ˆ๐‘ฅsecd๏Šจ.

  • Aโˆ’47๏€ผ7๐‘ฅ5+1๏ˆ+tanC
  • B2049๏€ผ7๐‘ฅ5+1๏ˆ+tanC
  • C47๏€ผ7๐‘ฅ5+1๏ˆ+tanC
  • Dโˆ’2049๏€ผ7๐‘ฅ5+1๏ˆ+tanC
  • Eโˆ’45๏€ผ7๐‘ฅ5+1๏ˆ+tanC

Q5:

Determine ๏„ธ48โˆ’6๐‘ฅโˆš16โˆ’2๐‘ฅ๐‘ฅ๏Žคd.

  • A53(16โˆ’2๐‘ฅ)+C
  • Bโˆ’56(16โˆ’2๐‘ฅ)+C
  • Cโˆ’158(16โˆ’2๐‘ฅ)+C
  • Dโˆ’32(16โˆ’2๐‘ฅ)+C

Q6:

Determine ๏„ธโˆ’116๐‘ฅโˆš๐‘ฅ๐‘ฅ๏Žขlnd.

  • Aโˆ’118(๐‘ฅ)+lnC๏Žฃ๏Žข
  • Bโˆ’118๐‘ฅ+lnC
  • C34(๐‘ฅ)+lnC๏Žฃ๏Žข
  • D43(๐‘ฅ)+lnC๏Žฃ๏Žข

Q7:

Determine ๏„ธ25๐‘ฅ+40๐‘ฅ+17โˆš5๐‘ฅ+4๐‘ฅ๏Šจd.

  • A25(5๐‘ฅ+4)+2โˆš5๐‘ฅ+4+๏Žค๏ŽกC
  • B215(5๐‘ฅ+4)+25โˆš5๐‘ฅ+4+๏Žข๏ŽกC
  • C225(5๐‘ฅ+4)+25โˆš5๐‘ฅ+4+๏Žค๏ŽกC
  • D225(5๐‘ฅ+4)+215(5๐‘ฅ+4)+๏Žค๏Žก๏Žข๏ŽกC

Q8:

Determine ๏„ธ๏€ป๏€นโˆ’24๐‘ฅ+306๐‘ฅ๏…๏€นโˆ’6๐‘ฅโˆ’56๐‘ฅ๏…๏‡๐‘ฅ๏Šฉ๏Šช๏Šซsincosd.

  • A16๏€นโˆ’6๐‘ฅโˆ’56๐‘ฅ๏…+๏Šช๏ŠฌcosC
  • B15๏€นโˆ’6๐‘ฅโˆ’56๐‘ฅ๏…+๏Šฉ๏ŠฌsinC
  • C๏€นโˆ’6๐‘ฅโˆ’56๐‘ฅ๏…+๏Šช๏ŠซcosC
  • D16๏€นโˆ’6๐‘ฅโˆ’56๐‘ฅ๏…+๏Šช๏ŠซcosC
  • E๏€พโˆ’3๐‘ฅ2โˆ’566๐‘ฅ๏Š+๏Šช๏ŠฌsinC

Q9:

Determine ๏„ธ๏€ป9๐‘ฅ2โˆ’22๐‘ฅ+8๏‡๏€ผ92๐‘ฅ2โˆ’42๐‘ฅ๏ˆ๐‘ฅsintancossecd๏Šฉ๏Šจ.

  • A13๏€ป9๐‘ฅ2โˆ’22๐‘ฅ+8๏‡+sintanC๏Šช
  • B12๏€ป9๐‘ฅ2โˆ’22๐‘ฅ+8๏‡+sintanC๏Šจ
  • C13๏€ป9๐‘ฅ2โˆ’22๐‘ฅ+8๏‡+sintanC๏Šจ
  • D14๏€ป9๐‘ฅ2โˆ’22๐‘ฅ+8๏‡+sintanC๏Šช

Q10:

Determine ๏„ธ(7โˆ’99๐‘ฅ)๐‘’๐‘ฅsind(๏Šญ๏—๏Šฐ๏Šฏ๏—)cos.

  • A๐‘’2+๏Šจ(๏Šญ๏—๏Šฐ๏Šฏ๏—)cosC
  • Bโˆ’9๐‘’+(๏Šญ๏—๏Šฐ๏Šฏ๏—)cosC
  • Cโˆ’๐‘’+(๏Šญ๏—๏Šฐ๏Šฏ๏—)cosC
  • D๐‘’+(๏Šญ๏—๏Šฐ๏Šฏ๏—)cosC

This lesson includes 109 additional questions and 835 additional question variations for subscribers.

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