Primitive of x by Power of a x + b/Also presented as
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Primitive of $x$ by Power of $a x + b$: Also presented as
This result is also seen presented in the form:
- $\ds \int x \paren {a x + b}^n \rd x = \frac {\paren {a x + b}^{n + 1} } {a^2} \paren {\frac {a x + b} {n + 2} - \frac b {n + 1} } + C$
where $n \ne - 1$ and $n \ne - 2$.
Also see
- Primitive of $x$ over $a x + b$ for the case when $n = -1$
- Primitive of $x$ over $\paren {a x + b}^2$ for the case when $n = -2$
Sources
- 1968: George B. Thomas, Jr.: Calculus and Analytic Geometry (4th ed.) ... (previous) ... (next): Front endpapers: A Brief Table of Integrals: $7$.