Primitive of x cubed over x fourth minus a fourth
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Theorem
- $\ds \int \frac {x^3 \rd x} {x^4 - a^4} = \frac {\ln \size {x^4 - a^4} } 4 + C$
Proof
\(\ds \frac \d {\d x} x^4\) | \(=\) | \(\ds 4 x^3\) | Primitive of Power | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \frac {x^3 \rd x} {x^4 - a^4}\) | \(=\) | \(\ds \frac {\ln \size {x^4 - a^4} } 4 + C\) | Primitive of Function under its Derivative |
$\blacksquare$
Sources
- 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 14$: Integrals involving $x^4 \pm a^4$: $14.321$