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Beliebt Rechnen >

integral of (sin(pix)-pixcos(pix))/(x^2)

Lösung

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

Lösung

- \frac{sin ( π x )}{x} + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{sin ( π x )}{x ^{2}} d x = - \frac{sin ( π x )}{x} + π Ci (π x)

\int \frac{π cos ( π x )}{x} d x = π Ci (π x)

= - \frac{sin ( π x )}{x} + π Ci (π x) - π Ci (π x)

Vereinfache

= - \frac{sin ( π x )}{x}

Füge eine Konstante zur Lösung hinzu

= - \frac{sin ( π x )}{x} + C

Graph

Beliebte Beispiele

integral of 4x^3-5x+5+1/x+3/(x^2)

\int 4 x^{3} - 5 x + 5 + \frac{1}{x} + \frac{3}{x ^{2}} d x

integral of (x^4+7)/(x^3+9x)

\int \frac{x ^{4} + 7}{x ^{3} + 9 x} d x

integral of 2/(sqrt(25-x^2))

\int \frac{2}{25 - x ^{2}} d x

integral of-x^3sin(x)

\int - x^{3} sin (x) d x

integral of (x^3)/(sqrt(x^2-64))

\int \frac{x ^{3}}{x ^{2} - 64} d x