integral of (x^5-9+6/(x^7))

Lösung

\int (x^{5} - 9 + \frac{6}{x ^{7}}) d x

\frac{x ^{6}}{6} - 9 x - \frac{1}{x ^{6}} + C

Schritte zur Lösung

\int x^{5} - 9 + \frac{6}{x ^{7}} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x^{5} d x - \int 9 d x + \int \frac{6}{x ^{7}} d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 9 d x = 9 x

\int \frac{6}{x ^{7}} d x = - \frac{1}{x ^{6}}

= \frac{x ^{6}}{6} - 9 x - \frac{1}{x ^{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} - 9 x - \frac{1}{x ^{6}} + C

\frac{d}{d x} (y + x) + x + y + 1 = 0

\int \frac{1}{- x ^{2} + 2 x + 8} d x

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a re a e^{8 x} - e^{2 x}, x = 1

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