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

Theorem

$\ds \int \frac {x^2 \rd x} {x^3 + a^3} = \frac 1 3 \ln \size {x^3 + a^3} + C$

Proof

\(\ds \map {\frac \d {\d x} } {x^3 + a^3}\)

\(=\)

\(\ds 3 x^2\)

Derivative of Power

\(\ds \leadsto \ \ \)

\(\ds \int \frac {x^2 \rd x} {x^3 + a^3}\)

\(=\)

\(\ds \frac 1 3 \ln \size {x^3 + a^3} + C\)

Primitive of Function under its Derivative

$\blacksquare$