integral of (x^4)/((1-x)^3)

Lösung

\int \frac{x ^{4}}{( 1 - x ) ^{3}} d x

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

Schritte zur Lösung

\int \frac{x ^{4}}{( 1 - x ) ^{3}} d x

Wende die partielle Integration an

= \frac{x ^{4}}{2 ( 1 - x ) ^{2}} - \int \frac{2 x ^{3}}{( 1 - x ) ^{2}} d x

\int \frac{2 x ^{3}}{( 1 - x ) ^{2}} d x = 2 (\frac{x ^{3}}{1 - x} + 3 (\frac{1}{2} x^{2} + x + ln ∣ - x + 1 ∣ + \frac{1}{2} - 2))

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e f (x) = (x^{4} + 3 x)^{- 1}

\frac{d ^{2}}{d x ^{2}} (\frac{2 x + 3}{3 x - 1})

\int \frac{1 - cos ( x )}{1 + sin ( x )} d x

\frac{d}{d x} (5^{l n (x)})

\frac{d}{d x} (\frac{x ^{6}}{3 - x ^{5}})