∫(1-u^2/c^2)^(-3/2)du

asked by guest
on Oct 24, 2024 at 5:10 am



You asked:

Evaluate the integral: \(\int{{\left( 1 - \frac{{u}^{2}}{{c}^{2}} \right)}^{\frac{-3}{2}}}du\)

MathBot Answer:

Antiderivative

\[\int{{\left( 1 - \frac{{u}^{2}}{{c}^{2}} \right)}^{\frac{-3}{2}}}du = C + \begin{cases} - \frac{i u}{\sqrt{-1 + \frac{u^{2}}{c^{2}}}} & \text{for}\: \left|{\frac{u^{2}}{c^{2}}}\right| > 1 \\\frac{u}{\sqrt{1 - \frac{u^{2}}{c^{2}}}} & \text{otherwise} \end{cases}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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