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Lesson Worksheet: Integrating Standard Functions Mathematics

In this worksheet, we will practice integrating standard functions, including polynomial, trigonometric, and exponential functions, and using the reverse chain rule to integrate functions of the form f(ax+b).

Q1:

Find the following integral: (𝑥+4)𝑥d.

  • A2𝑥+4𝑥+C
  • B2𝑥+4𝑥+C
  • C𝑥2+4𝑥+C
  • D2𝑥+𝑥4+C
  • E𝑥2+4𝑥+C

Q2:

Find the following integral: 2𝑥+3𝑒𝑥d.

  • A2𝑥+3𝑒+C
  • B2|𝑥|+3+lnC
  • C2|𝑥|+3𝑒+lnC
  • D2𝑥+3𝑒+C
  • E2𝑥+3+C

Q3:

Integrate the following function with respect to 𝑥: sincos𝑥𝑥.

  • AcossinC𝑥+𝑥+
  • B𝑥𝑥+cossinC
  • C𝑥+𝑥+cossinC
  • D𝑥𝑥+costanC
  • EcossinC𝑥𝑥+

Q4:

Evaluate the following integral, giving your answer as an exact value: 𝑥+2𝜋𝑥sind.

Q5:

Find the following integral: 𝑒+(2𝑥+1)𝑥d.

  • A12𝑒+16(2𝑥+1)+C
  • B2𝑒+6(2𝑥+1)+C
  • C12𝑒+8(2𝑥+1)+C
  • D12𝑒+18(2𝑥+1)+C
  • E12𝑒+12(2𝑥+1)+C

Q6:

Integrate the function csccot(10𝑥1)(10𝑥1) with respect to 𝑥.

  • A110(10𝑥1)+cscC
  • B10(10𝑥1)+cscC
  • C10(10𝑥1)+cotC
  • D110(10𝑥1)+cscC
  • E110(10𝑥1)+cotC

Q7:

Determine 4𝑥+6𝑥20𝑥coscosd.

  • A20𝑥+4𝑥+6𝑥+sintanC
  • B4𝑥+6𝑥+sintanC
  • C4𝑥+6𝑥+sintanC
  • D20𝑥4𝑥+6𝑥+sintanC
  • E20𝑥4𝑥+6𝑥+sintanC

Q8:

Given that 𝑘 is a positive constant and 𝑥+1𝑥𝑥=8+3dln, work out the exact value of 𝑘.

Q9:

Evaluate the following integral, giving your answer as an exact value: 𝑥𝑒𝑥d.

  • A3𝑒
  • B15𝑒
  • C17𝑒
  • D5𝑒
  • E4𝑒

Q10:

Determine 𝑥𝑥+1𝑥csctand.

  • AtancotC𝑥𝑥+
  • BtancotC𝑥+𝑥+
  • CcsccotC𝑥𝑥+
  • DcsccotC𝑥+𝑥+
  • E𝑥𝑥+tancotC

This lesson includes 90 additional question variations for subscribers.

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