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Integrate frac 1 - x x 3 with respect to x - JAMB Mathematics 1993 Question

Integrate (\frac{1 - x}{x^3}) with respect to x

A
\(\frac{x - x^2}{x^4}\) + k
B
\(\frac{4}{x^4} - \frac{3 + k}{x^3}\)
C
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
D
\(\frac{1}{3x^2} - \frac{1}{2x}\) + k
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Correct Option: C

(\int \frac{1 - x}{x^3})

= (\int^{1}{x^3} - \int^{x}{x^3})

= x-3 dx - x-2dx

= (\frac{1}{2x^2} + \frac{1}{x})

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