JAMB - Mathematics (1993 - No. 1)
Integrate \(\frac{1 - x}{x^3}\) with respect to x
\(\frac{x - x^2}{x^4}\) + k
\(\frac{4}{x^4} - \frac{3 + k}{x^3}\)
\(\frac{1}{x} - \frac{1}{2x^2}\) + k
\(\frac{1}{3x^2} - \frac{1}{2x}\) + k
Explicaţie
\(\int \frac{1 - x}{x^3}\)
= \(\int^{1}_{x^3} - \int^{x}_{x^3}\)
= x-3 dx - x-2dx
= \(\frac{1}{2x^2} + \frac{1}{x}\)
= \(\int^{1}_{x^3} - \int^{x}_{x^3}\)
= x-3 dx - x-2dx
= \(\frac{1}{2x^2} + \frac{1}{x}\)