integral of ((x^4))/(x-1)

Lösung

\int \frac{( x ^{4} )}{x - 1} d x

\frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + ln ∣ x - 1 ∣ + C

Schritte zur Lösung

\int \frac{x ^{4}}{x - 1} d x

Lange Division

\frac{x ^{4}}{x - 1} : x^{3} + x^{2} + x + 1 + \frac{1}{x - 1}

= \int x^{3} + x^{2} + x + 1 + \frac{1}{x - 1} 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^{3} d x + \int x^{2} d x + \int x d x + \int 1 d x + \int \frac{1}{x - 1} d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int x^{2} d x = \frac{x ^{3}}{3}

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

\int 1 d x = x

\int \frac{1}{x - 1} d x = ln ∣ x - 1 ∣

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + ln ∣ x - 1 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + \frac{x ^{3}}{3} + \frac{x ^{2}}{2} + x + ln ∣ x - 1 ∣ + C

\int cos^{4} (9 x) d x

f (x) = (ln (x))^{3}

a re a 8 - 3 x, 6 - x, 3

y^{^{''}} - 10 y^{^{'}} + 27 y = 0

\int x^{2} 7 x + 6 d x