Primitive of x cubed over x fourth plus a fourth/Proof 1

Theorem

$\ds \int \frac {x^3 \rd x} {x^4 + a^4} = \frac {\map \ln {x^4 + a^4} } 4 + C$

Proof

\(\ds \frac \d {\d x} x^4\)

\(=\)

\(\ds 4 x^3\)

Primitive of Power

\(\ds \leadsto \ \ \)

\(\ds \int \frac {x^3 \rd x} {x^4 + a^4}\)

\(=\)

\(\ds \frac 1 4 \ln \size {x^4 + a^4} + C\)

Primitive of Function under its Derivative

\(\ds \)

\(=\)

\(\ds \frac {\map \ln {x^4 + a^4} } 4 + C\)

Absolute Value of Even Power‎

$\blacksquare$