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Beliebt Rechnen >

integral of (xsin(x)+cos(x)-1)/(x^2)

Lösung

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

Lösung

- \frac{cos ( x )}{x} + \frac{1}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{sin ( x )}{x} d x = Si (x)

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

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

= Si (x) - \frac{cos ( x )}{x} - Si (x) - (- \frac{1}{x})

Vereinfache

= - \frac{cos ( x )}{x} + \frac{1}{x}

Füge eine Konstante zur Lösung hinzu

= - \frac{cos ( x )}{x} + \frac{1}{x} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(ln(x^2+3xy+2y^2))

\frac{\partial}{\partial x} (ln (x^{2} + 3 x y + 2 y^{2}))

7x^2y+(dy)/(dx)=4x^2

7 x^{2} y + \frac{d y}{d x} = 4 x^{2}

derivative of y^2-2xy+6x

\frac{d}{d x} (y^{2} - 2 x y + 6 x)

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

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

derivative f(x)=\sqrt[3]{-(-27)}

d er i v a t i v e f (x) = 3 - (- 27)