Primitive of Logarithm of a x
Jump to navigation
Jump to search
Theorem
- $\ds \int \ln a x \rd x = x \ln a x - x + C$
Proof
\(\ds \int \ln x \rd x\) | \(=\) | \(\ds x \ln x - x + C\) | Primitive of $\ln x$ | |||||||||||
\(\ds \leadsto \ \ \) | \(\ds \int \ln a x \rd x\) | \(=\) | \(\ds \frac 1 a \paren {a x \ln a x - a x} + C\) | Primitive of Function of Constant Multiple | ||||||||||
\(\ds \) | \(=\) | \(\ds x \ln a x - x + C\) | simplifying |
$\blacksquare$
Sources
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Back endpapers: A Brief Table of Integrals: $109$.