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Black Advanced Problems in Mathematics
Exam
Black Advanced Problems in Mathematics
Subject
Mathematics
Chapter
Indefinite and Definite Integration

Black Advanced Problems in Mathematics · Mathematics · Indefinite and Definite Integration

Given that ∫ (dx)/((1 + x^2)^n) = x 2(n - 1)(1 + x^2)^ n-1 + ((2n -...

Given that ∫dx(1+x2)n=x2(n−1)(1+x2)n−1+(2n−3)2(n−1)∫dx(1+x2)n−1\int \frac{dx}{(1 + x^2)^n} = \frac{x}{2(n - 1)(1 + x^2)^{n-1}} + \frac{(2n - 3)}{2(n - 1)} \int \frac{dx}{(1 + x^2)^{n-1}}. Find the value of ∫01dx(1+x2)4\int_0^1 \frac{dx}{(1 + x^2)^4} : (you may or may not use reduction formula given)

Options

  1. A1148+5π64\frac{11}{48} + \frac{5\pi}{64}
  2. B1148+5π32\frac{11}{48} + \frac{5\pi}{32}
  3. C124+5π64\frac{1}{24} + \frac{5\pi}{64}
  4. D196+5π32\frac{1}{96} + \frac{5\pi}{32}

Correct answer

A. 1148+5π64\frac{11}{48} + \frac{5\pi}{64}

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