integral of (y^5)/(1-y^4)

Lösung

\int \frac{y ^{5}}{1 - y ^{4}} d y

- \frac{y ^{2}}{2} + \frac{1}{4} (ln y^{2} + 1 - ln y^{2} - 1) + C

Schritte zur Lösung

\int \frac{y ^{5}}{1 - y ^{4}} d y

Lange Division

\frac{y ^{5}}{1 - y ^{4}} : - y + \frac{y}{- y ^{4} + 1}

= \int - y + \frac{y}{- y ^{4} + 1} d y

Wende die Summenregel an:

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

= - \int y d y + \int \frac{y}{- y ^{4} + 1} d y

\int y d y = \frac{y ^{2}}{2}

\int \frac{y}{- y ^{4} + 1} d y = \frac{1}{4} (ln y^{2} + 1 - ln y^{2} - 1)

= - \frac{y ^{2}}{2} + \frac{1}{4} (ln y^{2} + 1 - ln y^{2} - 1)

Füge eine Konstante zur Lösung hinzu

= - \frac{y ^{2}}{2} + \frac{1}{4} (ln y^{2} + 1 - ln y^{2} - 1) + C

\frac{\partial}{\partial t} (\frac{s}{t})

x \to 4 lim (2 x^{4} - x^{2} - 8 x)

\int_{0}^{2} x 3 4 + x^{2} d x

\frac{\partial}{\partial x} (\frac{3}{3 x + 5 y})

a re a 6 x^{2} ln (x), 24 ln (x)