integral of (x^4)/(sqrt((1-x^2)^3))

Lösung

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

\frac{x ^{5}}{1 - x ^{2}} + x^{3} 1 - x^{2} - \frac{3}{2} arcsin (x) + \frac{3}{4} sin (2 arcsin (x)) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= \frac{x ^{5}}{1 - x ^{2}} - \int \frac{4 x ^{4}}{1 - x ^{2}} d x

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

= \frac{x ^{5}}{1 - x ^{2}} - (- x^{3} 1 - x^{2} + \frac{3}{2} arcsin (x) - \frac{3}{4} sin (2 arcsin (x)))

Vereinfache

= \frac{x ^{5}}{1 - x ^{2}} + x^{3} 1 - x^{2} - \frac{3}{2} arcsin (x) + \frac{3}{4} sin (2 arcsin (x))

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{1 - x ^{2}} + x^{3} 1 - x^{2} - \frac{3}{2} arcsin (x) + \frac{3}{4} sin (2 arcsin (x)) + C

d er i v a t i v e (x + 2)^{2^{^{'}}}

\int 9 e^{2 x} d x

\int_{1}^{11 x^{15}} \frac{1}{t} d t

\frac{d}{d x} (\frac{2 x ^{5}}{5 + 3 x ^{4} + 6 x ^{3} + 2 x + 4})

z \to 0 lim ((2 z - 8) \frac{1}{3})