Worksheet: Integration by Substitution: Indefinite Integrals

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

Q1:

Determine 𝑥2𝑥−9𝑥d.

  • A−1122𝑥−9+C
  • B1162𝑥−9+C
  • C−𝑥82𝑥−9+C
  • D122𝑥−9+C

Q2:

Determine 𝑥𝑥+9𝑥d.

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

Q3:

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

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

Q4:

Determine −2𝑥(𝑥+8)𝑥d.

  • AlnC|𝑥+8|+8𝑥+8+
  • B−2|𝑥+8|+16𝑥+8+lnC
  • C−2|𝑥+8|−16𝑥+8+lnC
  • D−2|𝑥+8|−16𝑥+8+lnC

Q5:

Determine −24𝑥+306𝑥−6𝑥−56𝑥𝑥sincosd.

  • A16−6𝑥−56𝑥+cosC
  • B15−6𝑥−56𝑥+sinC
  • C−6𝑥−56𝑥+cosC
  • D16−6𝑥−56𝑥+cosC
  • E−3𝑥2−566𝑥+sinC

Q6:

Determine −116𝑥√𝑥𝑥lnd.

  • A−118(𝑥)+lnC
  • B−118𝑥+lnC
  • C34(𝑥)+lnC
  • D43(𝑥)+lnC

Q7:

Determine −49𝑥(9𝑥)𝑥lnd by using the substitution method.

  • A−12(9𝑥)+lnC
  • B227(9𝑥)+lnC
  • C1(9𝑥)+lnC
  • D−23(9𝑥)+lnC

Q8:

Determine (62𝑥−22𝑥)122𝑥−42𝑥𝑥sintancossecd.

  • A15(62𝑥−22𝑥)+cossecC
  • B22𝑥+22𝑥+cossecC
  • C16(122𝑥−42𝑥)+sintanC
  • D14122𝑥−42𝑥+cossecC
  • E16(62𝑥−22𝑥)+sintanC

Q9:

Determine 9𝑥2−22𝑥+892𝑥2−42𝑥𝑥sintancossecd.

  • A139𝑥2−22𝑥+8+sintanC
  • B129𝑥2−22𝑥+8+sintanC
  • C139𝑥2−22𝑥+8+sintanC
  • D149𝑥2−22𝑥+8+sintanC

Q10:

Determine (7−99𝑥)𝑒𝑥sind()cos.

  • A𝑒2+()cosC
  • B−9𝑒+()cosC
  • C−𝑒+()cosC
  • D𝑒+()cosC

Q11:

Determine 𝑥√4𝑥−19𝑥d.

  • A7208(4𝑥−19)+13396(4𝑥−19)+C
  • B7240(4𝑥−19)+133128(4𝑥−19)+C
  • C7208(4𝑥−19)+724(4𝑥−19)+C
  • D713(4𝑥−19)+1336(4𝑥−19)+C

Q12:

Determine (12𝑥−3)√4𝑥−1𝑥d.

  • A217(4𝑥−1)+C
  • B2417(4𝑥−1)+C
  • C23(4𝑥−1)+C
  • D2740(4𝑥−1)+C
  • E617(4𝑥−1)+C

Q13:

Using proper substitution, find √𝑥−24𝑥𝑥d.

  • A18√𝑥−2+C
  • B2√𝑥−2+C
  • C23√𝑥−2+C
  • D12√𝑥−2+C

Q14:

Determine 𝑥√6𝑥+7𝑥d.

  • A611(6𝑥+7)−425(6𝑥+7)+C
  • B178(6𝑥+7)−16(6𝑥+7)+C
  • C166(6𝑥+7)−15(6𝑥+7)+C
  • D166(6𝑥+7)−730(6𝑥+7)+C

Q15:

Determine 𝑥√5𝑥+9𝑥d.

  • A−15√5𝑥+9+C
  • B120√5𝑥+9+C
  • C15√5𝑥+9+C
  • D−115(5𝑥+9)+C
  • E110√5𝑥+9+C

Q16:

Determine 9𝑥−36𝑥+36(3𝑥−6)𝑥d.

  • A139(3𝑥−6)+C
  • B130(3𝑥−6)+C
  • C136(3𝑥−6)+C
  • D113(3𝑥−6)+C

Q17:

Determine 24−30𝑥√8−10𝑥𝑥d.

  • A−955(−10𝑥+8)+C
  • B−925(−10𝑥+8)+C
  • C1811(−10𝑥+8)+C
  • D−310(−10𝑥+8)+C

Q18:

Determine √2−7𝑥𝑥d.

  • A−221(−7𝑥+2)+C
  • B−514(−7𝑥+2)+C
  • C23(−7𝑥+2)+C
  • D−17(−7𝑥+2)+C

Q19:

Determine 48−6𝑥√16−2𝑥𝑥d.

  • A53(16−2𝑥)+C
  • B−56(16−2𝑥)+C
  • C−158(16−2𝑥)+C
  • D−32(16−2𝑥)+C

Q20:

Determine 2√2𝑥−9𝑥d.

  • A(2𝑥−9)+C
  • B2(2𝑥−9)+C
  • C−23(2𝑥−9)+C
  • D−(2𝑥−9)+C
  • E−2(2𝑥−9)+C

Q21:

Determine 𝑥4+7𝑥𝑥d.

  • A110(4𝑥+7)+C
  • B136(4𝑥+7)+C
  • C40(4𝑥+7)+C
  • D140(4𝑥+7)+C

Q22:

Determine 25𝑥+40𝑥+17√5𝑥+4𝑥d.

  • A25(5𝑥+4)+2√5𝑥+4+C
  • B215(5𝑥+4)+25√5𝑥+4+C
  • C225(5𝑥+4)+25√5𝑥+4+C
  • D225(5𝑥+4)+215(5𝑥+4)+C

Q23:

Determine −4𝑥+363𝑥√𝑥+99𝑥𝑥lnd.

  • A43√𝑥+99𝑥+lnC
  • B−83√𝑥+99𝑥+lnC
  • C83√𝑥+99𝑥+lnC
  • D−43√𝑥+99𝑥+lnC

Q24:

Determine 𝑥√10𝑥+3𝑥d.

  • A212510𝑥+3+C
  • B4310𝑥+3+C
  • C27510𝑥+3+C
  • D15010𝑥+3+C
  • E21510𝑥+3+C

Q25:

Determine (−12𝑥+26)√−12𝑥+26𝑥d.

  • A−130(−12𝑥+26)+C
  • B−118(−12𝑥+26)+C
  • C23(−12𝑥+26)+C
  • D52(−12𝑥+26)+C

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