PYQ Vault
EbooksTutor

Integral of 1 over (x - a)^p (x + b)^q with p + q = 2, by putting t = (x - a)/(x + b)

This type of question, asked 3 times: 2021 Paper 22, 8 Apr 2024, 23 Jan 2025. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    2021 Paper 22

    70
    The integral ∫1(x−1)3(x+2)54dx\int\frac{1}{\sqrt[4]{(x- 1)^{3}(x+ 2)^{5}}}dx is equal to : (where CC is a constant of integration)

    Tap an option to check your answer.

  2. Question 2

    8 Apr 2024

    180
    If ∫1(x−1)4(x+3)65dx=A(αx−1βx+3)B+C\int\frac{1}{\sqrt[5]{(x - 1)^{4}(x + 3)^{6}}}dx = A\left( \frac{\alpha x - 1}{\beta x + 3} \right)^{B}+ C, where CC is the constant of integration, then the value of α+β+20AB\alpha+\beta+ 20AB is

  3. Question 3

    23 Jan 2025

    52
    Let I(x)=∫dx(x−11)1113(x+15)1513I(x) = \int\frac{dx}{(x - 11)^{\frac{11}{13}}(x + 15)^{\frac{15}{13}}}. If I(37)−I(24)=14(1b113−1c113),b,c∈NI(37) - I(24) =\frac{1}{4}\left( \frac{1}{b^{\frac{1}{13}}}-\frac{1}{c^{\frac{1}{13}}} \right),b,c \in N, then 3(b+c)3(b + c) is equal to

    Tap an option to check your answer.