Rumus integral fungsi aljabar sederhana

Kita coba akan membuktikan rumus integral

$\int ax^{n} dx = \frac{a}{n+1}\: x^{n+1} + C$

$\begin{matrix} \\f\left ( x \right )=a{x^{n}}\rightarrow {f}'\left ( x \right )=na.x^{n-1} \\misal : n-1 = p \rightarrow n= p + 1 \\f\left ( x \right )=a{x^{p+1}}\rightarrow {f}'\left ( x \right )=\left ( p+1 \right )a.x^{p} \\misal: \left ( p+1 \right )a =q \rightarrow a=\frac{q}{p+1} \\f\left ( x \right )=\left (\frac{q}{p+1} \right ){x^{p+1}}\rightarrow {f}'\left ( x \right )=q.x^{p} \\\int {f}'\left ( x \right )dx = f\left ( x \right )+C \\\Leftrightarrow \int q.x^{p} dx = \left (\frac{q}{p+1} \right ){x^{p+1}}+C \end{matrix}$

$\int ax^{n} dx = \frac{a}{n+1}\: x^{n+1} + C$

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Rumus integral fungsi aljabar sederhana

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