Integrating hyperbolic and inverse functions

Integrating hyperbolic and inverse functions Quiz

Spec 4.1–2 · Edexcel International A Level Further Maths: Quiz

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5 questions, one answer each

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  1. 1. Find ∫sinh⁡3x dx\int\sinh3x\,dx.

    • A. 3cosh⁡3x+c3\cosh3x+c
    • B. cosh⁡3x+c\cosh3x+c
    • C. 13cosh⁡3x+c\frac13\cosh3x+c
    • D. −13cosh⁡3x+c-\frac13\cosh3x+c

  2. 2. Find ∫tanh⁡x dx\int\tanh x\,dx.

    • A. ln⁡cosh⁡x+c\ln\cosh x+c
    • B. sech⁡2x+c\operatorname{sech}^2x+c
    • C. ln⁡sinh⁡x+c\ln\sinh x+c
    • D. cosh⁡xsinh⁡x+c\cosh x\sinh x+c

  3. 3. Find ∫sech⁡22x dx\int\operatorname{sech}^22x\,dx.

    • A. tanh⁡2x+c\tanh2x+c
    • B. 2tanh⁡2x+c2\tanh2x+c
    • C. sech⁡2xtanh⁡2x+c\operatorname{sech}2x\tanh2x+c
    • D. 12tanh⁡2x+c\frac12\tanh2x+c

  4. 4. Find ∫xsinh⁡x dx\int x\sinh x\,dx.

    • A. xsinh⁡x−cosh⁡x+cx\sinh x-\cosh x+c
    • B. xcosh⁡x−sinh⁡x+cx\cosh x-\sinh x+c
    • C. xcosh⁡x+sinh⁡x+cx\cosh x+\sinh x+c
    • D. 12x2cosh⁡x+c\frac12x^2\cosh x+c

  5. 5. Find ∫arctan⁡x dx\int\arctan x\,dx.

    • A. 11+x2+c\frac{1}{1+x^2}+c
    • B. xarctan⁡x−ln⁡(1+x2)+cx\arctan x-\ln\left(1+x^2\right)+c
    • C. xarctan⁡x−12ln⁡(1+x2)+cx\arctan x-\frac12\ln\left(1+x^2\right)+c
    • D. xarctan⁡x+12ln⁡(1+x2)+cx\arctan x+\frac12\ln\left(1+x^2\right)+c

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