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Beliebt Rechnen >

integral of (sin(x)-xcos(x))/(sin^2(x))

Lösung

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

Lösung

x cot (x) cos (x) + x sin (x) + C

Schritte zur Lösung

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

Wende die partielle Integration an

= - cot (x) (sin (x) - x cos (x)) - \int - x sin (x) cot (x) d x

\int - x sin (x) cot (x) d x = - x sin (x) - cos (x)

= - cot (x) (sin (x) - x cos (x)) - (- x sin (x) - cos (x))

Vereinfache

- cot (x) (sin (x) - x cos (x)) - (- x sin (x) - cos (x)) : x cot (x) cos (x) + x sin (x)

= x cot (x) cos (x) + x sin (x)

Füge eine Konstante zur Lösung hinzu

= x cot (x) cos (x) + x sin (x) + C

Graph

Beliebte Beispiele

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

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

integral of (x+2)*sin(x^2+4x-6)

\int (x + 2) \cdot sin (x^{2} + 4 x - 6) d x

integral of sec^3(x)tan^7(x)

\int sec^{3} (x) tan^{7} (x) d x

integral of (4-sin(t/2))^2cos(t/2)

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

integral of sin^4(y)cos^5(y)

\int sin^{4} (y) cos^{5} (y) d y