Worksheet: Indefinite Integrals: Exponential and Reciprocal Functions

In this worksheet, we will practice finding the indefinite integral of exponential and reciprocal functions (1/x).

Q1:

Determine 2𝑒𝑥𝑥d.

  • A2𝑒91318
  • B2𝑒52
  • C2𝑒3
  • D2𝑒9119

Q2:

Determine 55𝑒𝑛d.

  • A25𝑒+C
  • B5𝑒+C
  • C55𝑒+C
  • D5𝑒+C

Q3:

Evaluate (𝑥+2𝑒)𝑥d.

  • A2𝑒+1
  • B2𝑒11+𝑒+2
  • C2+11+𝑒+2𝑒
  • D1+2𝑒
  • E2+1𝑒+2𝑒

Q4:

Determine 8𝑒𝑒+97𝑒𝑥d.

  • A87𝑒𝑒7+97𝑒+C
  • B47𝑒𝑒7+97𝑒+C
  • C47𝑒𝑒797𝑒+C
  • D167𝑒𝑒797𝑒+C

Q5:

Given that 𝑓(𝑥)=5𝑒+2𝑥, find 𝑓(𝑥).

  • A𝑓(𝑥)=54𝑒+𝑥3+C
  • B𝑓(𝑥)=5𝑒+2𝑥+𝑥+CD
  • C𝑓(𝑥)=516𝑒+𝑥21+𝑥+CD
  • D𝑓(𝑥)=5𝑒+𝑥21+𝑥+CD
  • E𝑓(𝑥)=5𝑒+2𝑥+C

Q6:

Determine 3𝑒+8𝑥𝑥d.

  • A3𝑒5+1775
  • B3𝑒+33
  • C3𝑒+69
  • D3𝑒5+3575

Q7:

Determine 497𝑥+5𝑥d.

  • A49𝑥57|𝑥|+lnC
  • B7|7𝑥+5|+lnC
  • C7|7𝑥+5|+lnC
  • D49𝑥549|𝑥|+lnC

Q8:

Determine 23𝑥7𝑥lnd.

  • A237|𝑥|+lnlnC
  • B237|𝑥|+lnlnC
  • C237|𝑥|+lnlnC
  • D237|𝑥|+lnlnC

Q9:

Determine 4𝜋𝑒𝑥d.

  • A4𝜋3𝑒+C
  • B4𝜋𝑒+C
  • C4𝜋3𝑒+C
  • D4𝜋3𝑒+C

Q10:

Determine (2𝑥5)𝑥𝑥d.

  • A4𝑥+20𝑥+25|𝑥|+lnC
  • B4𝑥+20𝑥+25|𝑥|+lnC
  • C2𝑥+20𝑥+25|𝑥|+lnC
  • D2𝑥+20𝑥+25|𝑥|+lnC

Q11:

Determine 8𝑥+4𝑥𝑥d.

  • A4𝑥5+4|𝑥|+lnC
  • B4𝑥5+4|𝑥|+lnC
  • C8𝑥+4|𝑥|+lnC
  • D8𝑥+4|𝑥|+lnC

Q12:

Determine 9𝑒+52𝑒𝑥d.

  • A81𝑒+45𝑥+254𝑒+C
  • B274𝑒+45𝑥2548𝑒+C
  • C34𝑒+45𝑥548𝑒+C
  • D274𝑒+45𝑥+2548𝑒+C

Q13:

Determine 8𝑥+7𝑒𝑥d.

  • A8𝑥3𝑒+1+7𝑒+C
  • B8𝑥3𝑒+178𝑒+C
  • C78𝑒+83𝑒𝑥+C
  • D78𝑒+83𝑒𝑥+C

Q14:

Determine2𝑥d.

  • A292+lnC
  • B22+lnC
  • C22+lnC
  • D292+lnC

Q15:

Determine 57𝑒𝑥d.

  • A157𝑒+C
  • B57𝑒+C
  • C57𝑒+C
  • D521𝑒+C

Q16:

Determine 6𝑒𝑦d.

  • A60𝑒+C
  • B0.6𝑒+C
  • C60𝑒+C
  • D6𝑒+C

Q17:

Determine 7𝑥36𝑥𝑥d.

  • A7𝑥1212|𝑥|+lnC
  • B7𝑥312|𝑥|+lnC
  • C7𝑥1212|𝑥|+lnC
  • D7𝑥612|𝑥|+lnC

Q18:

Determine 7𝑒𝑥+2𝑥𝑒𝑥d.

  • A7𝑒|𝑥|+8𝑥𝑒+lnC
  • B7𝑒|𝑥|+2𝑥5𝑒+lnC
  • C7𝑒|𝑥|+2𝑥5𝑒+lnC
  • D7𝑒|𝑥|+𝑥2𝑒+lnC

Q19:

Determine 27𝑥𝑥d.

  • A27|𝑥|+lnC
  • B27|𝑥|+lnC
  • C27|𝑥|+lnC
  • D27|𝑥|+lnC

Q20:

Determine the most general antiderivative 𝐹(𝑥) of the function 𝑓, given that 𝑓(𝑥)=52+4𝑥.

  • A𝐹(𝑥)=5𝑥2+|𝑥|+lnC
  • B𝐹(𝑥)=𝑥2+|𝑥|+lnC
  • C𝐹(𝑥)=5𝑥+4|𝑥|+lnC
  • D𝐹(𝑥)=5𝑥2+4|𝑥|+lnC
  • E𝐹(𝑥)=𝑥2+4|𝑥|+lnC

Q21:

Find, if possible, an antiderivative 𝐹 of 𝑓(𝑥)=12𝑥1 that satisfies the conditions 𝐹(0)=1 and 𝐹(1)=1.

  • ANo such antiderivative exists.
  • B𝐹(𝑥)=12(12𝑥)+1𝑥<12,12(2𝑥1)1𝑥>12lnforlnfor

Q22:

Determine the most general antiderivative of the function 𝑟(𝜃)=3𝑒+2𝜃𝜃tansec.

  • A𝑅(𝜃)=3𝑒+2𝜃+secC
  • B𝑅(𝜃)=3𝑒+𝜃𝜃+tansecC
  • C𝑅(𝜃)=3𝑒𝜃+1+2𝜃+secC
  • D𝑅(𝜃)=𝑒(3𝜃+3)+2𝜃+secC
  • E𝑅(𝜃)=3𝑒𝜃+1+𝜃𝜃+tansecC

Q23:

Determine 54𝑥𝑥lnd.

  • A145|𝑥|+lnlnC
  • B14(𝑥+5)+lnC
  • ClnlnC5|4𝑥|+
  • D145𝑥+lnC

Q24:

Determine 3𝑥+79𝑥𝑥d.

  • A9𝑥2+7𝑥3+4981|𝑥|+lnC
  • B9𝑥2+14𝑥3+4981|𝑥|+lnC
  • C9𝑥+14𝑥3+4981|𝑥|+lnC
  • D3𝑥2+14𝑥3+79|𝑥|+lnC

Q25:

Determine 74𝑥6𝑒𝑥d.

  • A74|𝑥|+3𝑒+lnC
  • B74|𝑥|6𝑒+lnC
  • C74|𝑥|+3𝑒+lnC
  • D7|4𝑥|+3𝑒+lnC

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