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MATHEMATICS

JAMB 2013 - Question 38

Mathematics 2013 JAMB Past Questions - Question 38: integrate (1 + X)/x³ dx

integrate (1 + X)/x³ dx

A: 2x²-1/x+k

B: -1/2x² -1/x+k

C: -x²/2-1/x+k

D: x²-1/x+k

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Correct Answer

Explanation

To integrate the expression (1 + x)/x³, we can use the method of partial fractions. First, let's rewrite the expression as a sum of two fractions:(1 + x)/x³ = 1/x³ + x/x³Now, we can integrate each fraction separately:∫(1/x³) dx = ∫x^(-3) dx = -x^(-2)/2 + C₁∫(x/x³) dx = ∫x^(-2) dx = -x^(-1)/1 + C₂Where C₁ and C₂ are constants of integration.Combining the results, we have:∫(1 + x)/x³ dx = -x^(-2)/2 - x^(-1) + CTherefore, the integral of (1 + x)/x³ is -x^(-2)/2 - x^(-1) + C, where C is the constant of integration.