Primitive of x by Exponential of a x/Also presented as
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Primitive of $x e^{a x} \rd x$: Also presented as
This result is also seen presented in the form:
- $\ds \int x e^{a x} \rd x = \frac {e^{a x} } {a^2} \paren {a x - 1} + C$
Proof
\(\ds \frac {e^{a x} } {a^2} \paren {a x - 1}\) | \(=\) | \(\ds \frac {e^{a x} } a \cdot \dfrac 1 a \paren {a x - 1}\) | ||||||||||||
\(\ds \) | \(=\) | \(\ds \frac {e^{a x} } a \paren {x - \dfrac 1 a}\) |
$\blacksquare$
Sources
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Back endpapers: A Brief Table of Integrals: $104$.