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Beliebt Rechnen >

integral of 1/(x^8+x)

Lösung

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

Lösung

\frac{1}{7} ln x^{7} - \frac{1}{7} ln x^{7} + 1 + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{1}{x ^{7} + 1} - \int - \frac{8 x ^{7} + 1}{x ( x ^{7} + 1 ) ^{2}} d x

\int - \frac{8 x ^{7} + 1}{x ( x ^{7} + 1 ) ^{2}} d x = - \frac{1}{7} ln x^{7} + \frac{1}{7} ln x^{7} + 1 + \frac{1}{x ^{7} + 1}

= \frac{1}{x ^{7} + 1} - (- \frac{1}{7} ln x^{7} + \frac{1}{7} ln x^{7} + 1 + \frac{1}{x ^{7} + 1})

Vereinfache

= \frac{1}{7} ln x^{7} - \frac{1}{7} ln x^{7} + 1

Füge eine Konstante zur Lösung hinzu

= \frac{1}{7} ln x^{7} - \frac{1}{7} ln x^{7} + 1 + C

Graph

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