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Beliebt Rechnen >

integral of (sqrt(x^4+x^{-4)+2})/(x^3)

Lösung

\int \frac{x ^{4} + x ^{- 4} + 2}{x ^{3}} d x

Lösung

ln ∣ x ∣ - \frac{1}{4 x ^{4}} + C

Schritte zur Lösung

\int \frac{x ^{4} + x ^{- 4} + 2}{x ^{3}} d x

Vereinfache

x^{4} : x^{3} x

= \int \frac{x ^{3} x + x ^{- 4} + 2}{x ^{3}} d x

Vereinfache

\frac{x ^{3} x + x ^{- 4} + 2}{x ^{3}} : \frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 )}{x ^{5}}

= \int \frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 )}{x ^{5}} d x

Multipliziere aus

\frac{( x ^{2} + 2 x + 1 ) ( x ^{2} - 2 x + 1 )}{x ^{5}} : \frac{1}{x} + \frac{1}{x ^{5}}

= \int \frac{1}{x} + \frac{1}{x ^{5}} 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 \frac{1}{x} d x + \int \frac{1}{x ^{5}} d x

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ - \frac{1}{4 x ^{4}}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - \frac{1}{4 x ^{4}} + C

Graph

Beliebte Beispiele

tangent sqrt(4x+84)

t an g e n t 4 x + 84

derivative arcsec(6x)

d er i v a t i v e arcsec (6 x)

(\partial)/(\partial x)(e^xg)

\frac{\partial}{\partial x} (e^{x} g)

36y^{''}-36y^'-7y=0

36 y^{^{''}} - 36 y^{^{'}} - 7 y = 0

limit as x approaches a of f(x)

x \to a lim (f (x))