Lesson 1.08h

1.08h Integration by substitution Quiz: OCR Maths, Unit 8

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson 1.08h, Integration by substitution: 20 multiple choice questions for the OCR Maths (H240), Unit 8: Integration, written with Revision Ninja.

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The 20 questions

  1. Which result is the integral of f'(x)(f(x))^n with n not equal to -1?

    • (f(x))^(n+1)/(n+1) + c
    • f'(x)(f(x))^(n+1) + c
    • (f(x))^n/n + c
    • n (f(x))^(n-1) + c

  2. What is the integral of f'(x)/f(x)?

    • ln|f(x)| + c
    • f'(x) ln f(x) + c
    • 1/f(x) + c
    • ln f'(x) + c

  3. Which result is the integral of tan x?

    • cot x + c
    • ln|sec x| + c
    • ln|sin x| + c
    • sec^2 x + c

  4. Which differentiation rule is integration by substitution designed to reverse?

    • Quotient rule
    • Chain rule
    • Power rule
    • Product rule

  5. Find the integral of 2x(x^2 + 3)^4 with respect to x.

    • (x^2 + 3)^5 + c
    • 2(x^2 + 3)^5/5 + c
    • (x^2 + 3)^4/4 + c
    • (x^2 + 3)^5/5 + c

  6. Find the integral of x(x^2 + 1)^3 with respect to x.

    • (x^2 + 1)^4/2 + c
    • (x^2 + 1)^4/4 + c
    • (x^2 + 1)^4/8 + c
    • x^2 (x^2 + 1)^4/8 + c

  7. Find the integral of 3x^2/(x^3 + 1) with respect to x.

    • ln|x^3 + 1| + c
    • 1/(x^3 + 1)^2 + c
    • ln|x| + c
    • ln|3x^2| + c

  8. Find the integral of 4x/(x^2 + 5) with respect to x.

    • ln(x^2 + 5) + c
    • 4 ln(x^2 + 5) + c
    • 2 ln(x^2 + 5) + c
    • 2 ln x + c

  9. Find the integral of (2x + 1)^5 with respect to x.

    • (2x + 1)^6 + c
    • (2x + 1)^6/12 + c
    • (2x + 1)^6/2 + c
    • (2x + 1)^6/6 + c

  10. Evaluate the integral from 0 to 1 of 2x(x^2 + 1) dx.

    • 1
    • 5/2
    • 2
    • 3/2

  11. Evaluate the integral from 0 to 1 of x e^(x^2) dx.

    • e - 1
    • (e - 1)/2
    • e/2
    • 1/2

  12. Find the integral of cos^2 x sin x with respect to x.

    • cos^3 x/3 + c
    • -cos^3 x/3 + c
    • sin^3 x/3 + c
    • -cos^3 x + c

  13. Find the integral of x/(x^2 + 1)^2 with respect to x.

    • 1/(2(x^2 + 1)) + c
    • ln|x^2 + 1| + c
    • -1/(x^2 + 1) + c
    • -1/(2(x^2 + 1)) + c

  14. Evaluate the integral from 0 to 2 of x(x^2 + 1)^3 dx.

    • 78
    • 312
    • 156
    • 39

  15. With u = 2x + 1, how does the integral of (2x + 1)^3 dx change?

    • (1/2) u^3 du
    • u^3 du
    • (1/2) u^4 du
    • 2u^3 du

  16. Find the integral of cos x / sin x with respect to x.

    • ln|cos x| + c
    • ln|sin x| + c
    • -ln|sin x| + c
    • cot x + c

  17. Find the integral of x^2 (x^3 + 1)^2 with respect to x.

    • (x^3 + 1)^3/9 + c
    • (x^3 + 1)^3/3 + c
    • (x^3 + 1)^2/9 + c
    • (x^3 + 1)^3 + c

  18. Find the integral of e^x/(1 + e^x) with respect to x.

    • ln(1 + e^x) + c
    • 1/(1 + e^x) + c
    • ln(e^x) + c
    • e^x/(1 + e^x)^2 + c

  19. Integration by substitution is the reverse of which rule of differentiation?

    • Power rule
    • Product rule
    • Chain rule
    • Quotient rule

  20. Which integrand has the form f'(x)/f(x)?

    • 2x/(x^2 + 3)
    • x^2/(x^2 + 3)
    • 1/(x^2 + 3)
    • x/(x + 3)

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