Primitive of x cubed over x fourth minus a fourth

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 $x^4 \pm a^4$: $14.321$