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Beliebt Rechnen >

integral of ((x^2cos(x)-2xsin(x)))/(x^4)

Lösung

\int \frac{( x ^{2} cos ( x ) - 2 x sin ( x ) )}{x ^{4}} d x

Lösung

\frac{sin ( x )}{x ^{2}} + C

Schritte zur Lösung

\int \frac{x ^{2} cos ( x ) - 2 x sin ( x )}{x ^{4}} d x

Multipliziere aus

\frac{x ^{2} cos ( x ) - 2 x sin ( x )}{x ^{4}} : \frac{cos ( x )}{x ^{2}} - \frac{2 sin ( x )}{x ^{3}}

= \int \frac{cos ( x )}{x ^{2}} - \frac{2 sin ( x )}{x ^{3}} 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{cos ( x )}{x ^{2}} d x - \int \frac{2 sin ( x )}{x ^{3}} d x

\int \frac{cos ( x )}{x ^{2}} d x = - \frac{cos ( x )}{x} - Si (x)

\int \frac{2 sin ( x )}{x ^{3}} d x = - \frac{sin ( x )}{x ^{2}} - \frac{cos ( x )}{x} - Si (x)

= - \frac{cos ( x )}{x} - Si (x) - (- \frac{sin ( x )}{x ^{2}} - \frac{cos ( x )}{x} - Si (x))

Vereinfache

= \frac{sin ( x )}{x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{sin ( x )}{x ^{2}} + C

Graph

Beliebte Beispiele

integral of (x^2+1)/(x^3+x^2-x-1)

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

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\int (- \frac{3}{x + 2} - \frac{4}{x + 5}) d x

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

integral of e^{2x}4x

\int e^{2 x} 4 x d x

integral of sqrt(-x^2-2x+3)

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