Lesson Worksheet: Integration by Substitution: Indefinite Integrals Mathematics

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

Q1:

Determine 8𝑥(8𝑥+9)𝑥d by using the substitution method.

  • A124(8𝑥+9)+C
  • B916(8𝑥+9)+C
  • C132(8𝑥+9)38(8𝑥+9)+C
  • D124(8𝑥+9)916(8𝑥+9)+C
  • E124(8𝑥+9)916(8𝑥+9)+C

Q2:

Determine 𝑥𝑥+9𝑥d.

  • A16𝑥+9+C
  • B148𝑥+9+C
  • C𝑥48𝑥+9+C
  • D18𝑥+9+C

Q3:

Determine 𝑥11(𝑥2)𝑥d.

  • A17(𝑥2)+1(𝑥2)+C
  • B17(𝑥2)+1(𝑥2)+C
  • C17(𝑥2)+98(𝑥2)+C
  • D17(𝑥2)+910(𝑥2)+C

Q4:

Determine 477𝑥5+1𝑥secd.

  • A477𝑥5+1+tanC
  • B20497𝑥5+1+tanC
  • C477𝑥5+1+tanC
  • D20497𝑥5+1+tanC
  • E457𝑥5+1+tanC

Q5:

Determine 486𝑥162𝑥𝑥d.

  • A53(162𝑥)+C
  • B56(162𝑥)+C
  • C158(162𝑥)+C
  • D32(162𝑥)+C

Q6:

Determine 116𝑥𝑥𝑥lnd.

  • A118(𝑥)+lnC
  • B118𝑥+lnC
  • C34(𝑥)+lnC
  • D43(𝑥)+lnC

Q7:

Determine 25𝑥+40𝑥+175𝑥+4𝑥d.

  • A25(5𝑥+4)+25𝑥+4+C
  • B215(5𝑥+4)+255𝑥+4+C
  • C225(5𝑥+4)+255𝑥+4+C
  • D225(5𝑥+4)+215(5𝑥+4)+C

Q8:

Determine 24𝑥+306𝑥6𝑥56𝑥𝑥sincosd.

  • A166𝑥56𝑥+cosC
  • B156𝑥56𝑥+sinC
  • C6𝑥56𝑥+cosC
  • D166𝑥56𝑥+cosC
  • E3𝑥2566𝑥+sinC

Q9:

Determine 9𝑥222𝑥+892𝑥242𝑥𝑥sintancossecd.

  • A139𝑥222𝑥+8+sintanC
  • B129𝑥222𝑥+8+sintanC
  • C139𝑥222𝑥+8+sintanC
  • D149𝑥222𝑥+8+sintanC

Q10:

Determine (799𝑥)𝑒𝑥sind()cos.

  • A𝑒2+()cosC
  • B9𝑒+()cosC
  • C𝑒+()cosC
  • D𝑒+()cosC

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