de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (2x^2+3x-5)sin(x)

Lösung

\int (2 x^{2} + 3 x - 5) sin (x) d x

Lösung

- 2 x^{2} cos (x) + 4 x sin (x) - 3 x cos (x) + 9 cos (x) + 3 sin (x) + C

Schritte zur Lösung

\int (2 x^{2} + 3 x - 5) sin (x) d x

Multipliziere aus

(2 x^{2} + 3 x - 5) sin (x) : 2 x^{2} sin (x) + 3 x sin (x) - 5 sin (x)

= \int 2 x^{2} sin (x) + 3 x sin (x) - 5 sin (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 2 x^{2} sin (x) d x + \int 3 x sin (x) d x - \int 5 sin (x) d x

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

\int 3 x sin (x) d x = 3 (- x cos (x) + sin (x))

\int 5 sin (x) d x = - 5 cos (x)

= 2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + 3 (- x cos (x) + sin (x)) - (- 5 cos (x))

Vereinfache

2 (- x^{2} cos (x) + 2 (x sin (x) + cos (x))) + 3 (- x cos (x) + sin (x)) - (- 5 cos (x)) : - 2 x^{2} cos (x) + 4 x sin (x) - 3 x cos (x) + 9 cos (x) + 3 sin (x)

= - 2 x^{2} cos (x) + 4 x sin (x) - 3 x cos (x) + 9 cos (x) + 3 sin (x)

Füge eine Konstante zur Lösung hinzu

= - 2 x^{2} cos (x) + 4 x sin (x) - 3 x cos (x) + 9 cos (x) + 3 sin (x) + C

Graph

Beliebte Beispiele

tangent f(x)=3x^3-x^2+7,\at x=2

t an g e n t f (x) = 3 x^{3} - x^{2} + 7, at x = 2

steigung 6x-x^2

s l o p e 6 x - x^{2}

integral from 1 to 5 of x/(sqrt(x-1))

\int_{1}^{5} \frac{x}{x - 1} d x

integral of-2csc^2(x)cot(x)

\int - 2 csc^{2} (x) cot (x) d x

derivative of (5x/(x+3))

\frac{d}{d x} (\frac{5 x}{x + 3})