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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

If ∫ (dx)/(x^4 (1 + x^3)^2) = a | (1 + x^3)/(x^3) | + (b)/(x^3) +...

If ∫dxx4(1+x3)2=aln⁡∣1+x3x3∣+bx3+c1+x3+d\int \frac{dx}{x^4 (1 + x^3)^2} = a \ln \left| \frac{1 + x^3}{x^3} \right| + \frac{b}{x^3} + \frac{c}{1 + x^3} + d, then (where dd is arbitrary constant)

Options

  1. Aa=13,b=13,c=13a = \frac{1}{3}, b = \frac{1}{3}, c = \frac{1}{3}
  2. Ba=23,b=−13,c=13a = \frac{2}{3}, b = -\frac{1}{3}, c = \frac{1}{3}
  3. Ca=23,b=−13,c=−13a = \frac{2}{3}, b = -\frac{1}{3}, c = -\frac{1}{3}
  4. Da=23,b=13,c=13a = \frac{2}{3}, b = \frac{1}{3}, c = \frac{1}{3}

Correct answer

C. a=23,b=−13,c=−13a = \frac{2}{3}, b = -\frac{1}{3}, c = -\frac{1}{3}

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