Integrate ≤ft(x - \;1/x)² with respect to x.

Correct Answer is : x33−2x− 1x+c\;{x³}{3} - 2x - \;1/x + c3x3−2x−x1+c

\;{x³}{3} - x {\;{1}{x³}} + c

\;{x³}{3} - 2x + \;{1}{x³} + c

Correct Answer is : x33−2x− 1x+c\;{x³}{3} - 2x - \;1/x + c3x3−2x−x1+c

Test Index

WAEC Further Mathematics 2014 Paper

Question : 22

Total: 40

Integrate

\left(x - \;\frac{1}{x}\right)^{2}

with respect to x.

Solution:

$\left(x - \;\frac{1}{x}\right)^{2} = x^{2} - 2 + \;\frac{1}{x^{2}}$

$\int \left(x^{2} + \;\frac{1}{x^{2}} - 2\right) \, dx$

= $\int \left(x^{2} + x^{-2} - 2\right) \, dx$

= $\;\frac{x^{3}}{3} - 2x - \;\frac{1}{x}$

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