PYQ Vault
EbooksTutor

Writing the numerator as A times the denominator plus B times its derivative

This type of question, asked 2 times: 2021 Paper 21, 9 Apr 2024. All 2 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 21

    90
    If ∫2ex+3e−x4ex+7e−xdx=114(ux+vlog⁡e(4ex+7e−x))+C\int\frac{2e^{x}+ 3e^{-x}}{4e^{x}+ 7e^{-x}}dx=\frac{1}{14}\left( ux+v\log_{e}\left( 4e^{x}+ 7e^{-x} \right) \right)+C, where CC is a constant of integration, then u+vu+v is equal to

  2. Question 2

    9 Apr 2024

    67
    Let ∫2−tan⁡x3+tan⁡xdx=12(αx+log⁡e∣βsin⁡x+γcos⁡x∣)+C\int\frac{2 - \tan x}{3 + \tan x}dx =\frac{1}{2}\left( \alpha x +\log_{e}|\beta \sin x + \gamma \cos x| \right)+ C , where CC is the constant of integration. Then α+γβ\alpha +\frac{\gamma}{\beta} is equal to:

    Tap an option to check your answer.