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Beliebt Rechnen >

integral of-2ysin^2(y)

Lösung

\int - 2 y sin^{2} (y) d y

Lösung

- y^{2} + \frac{1}{2} y sin (2 y) + \frac{y ^{2}}{2} + \frac{1}{4} cos (2 y) + C

Schritte zur Lösung

\int - 2 y sin^{2} (y) d y

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int y sin^{2} (y) d y

Wende die partielle Integration an

= - 2 (\frac{1}{2} y (y - \frac{1}{2} sin (2 y)) - \int \frac{1}{2} (y - \frac{1}{2} sin (2 y)) d y)

\int \frac{1}{2} (y - \frac{1}{2} sin (2 y)) d y = \frac{1}{2} (\frac{y ^{2}}{2} + \frac{1}{4} cos (2 y))

= - 2 (\frac{1}{2} y (y - \frac{1}{2} sin (2 y)) - \frac{1}{2} (\frac{y ^{2}}{2} + \frac{1}{4} cos (2 y)))

Vereinfache

- 2 (\frac{1}{2} y (y - \frac{1}{2} sin (2 y)) - \frac{1}{2} (\frac{y ^{2}}{2} + \frac{1}{4} cos (2 y))) : - y^{2} + \frac{1}{2} y sin (2 y) + \frac{y ^{2}}{2} + \frac{1}{4} cos (2 y)

= - y^{2} + \frac{1}{2} y sin (2 y) + \frac{y ^{2}}{2} + \frac{1}{4} cos (2 y)

Füge eine Konstante zur Lösung hinzu

= - y^{2} + \frac{1}{2} y sin (2 y) + \frac{y ^{2}}{2} + \frac{1}{4} cos (2 y) + C

Graph

Beliebte Beispiele

integral of sin(4x)sin(5x)

\int sin (4 x) sin (5 x) d x

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\int \frac{y ^{2} e ^{y^{3}}}{2} d y

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

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