de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (1-x^8)/(x(1+x^8))

Lösung

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

Lösung

ln (x) - \frac{1}{4} ln 1 + x^{8} + C

Schritte zur Lösung

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

Multipliziere aus

\frac{1 - x ^{8}}{x ( 1 + x ^{8} )} : \frac{1}{x ( 1 + x ^{8} )} - \frac{x ^{8}}{x ( 1 + x ^{8} )}

Wende die Summenregel an:

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

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

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

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

= \frac{1}{8} (8 ln (x) - ln 1 + x^{8}) - \frac{1}{8} ln 1 + x^{8}

Vereinfache

\frac{1}{8} (8 ln (x) - ln 1 + x^{8}) - \frac{1}{8} ln 1 + x^{8} : ln (x) - \frac{1}{4} ln 1 + x^{8}

= ln (x) - \frac{1}{4} ln 1 + x^{8}

Füge eine Konstante zur Lösung hinzu

= ln (x) - \frac{1}{4} ln 1 + x^{8} + C

Graph

Beliebte Beispiele

integral of sqrt(1+(9x^{1/2))^2}

\int 1 + (9 x^{\frac{1}{2}})^{2} d x

integral of 2^{-2x}

\int 2^{- 2 x} d x

integral of (10x^2-2x-6)/(x^3-x^2-2x)

\int \frac{10 x ^{2} - 2 x - 6}{x ^{3} - x ^{2} - 2 x} d x

integral of ((sqrt(x)-1)^2)/x

\int \frac{( x - 1 ) ^{2}}{x} d x

integral of xsqrt(3x+8)

\int x 3 x + 8 d x