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Beliebt Rechnen >

integral of (2cos(x)-3sin(x)+x)

Lösung

\int (2 cos (x) - 3 sin (x) + x) d x

Lösung

2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int 2 cos (x) - 3 sin (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 2 cos (x) d x - \int 3 sin (x) d x + \int x d x

\int 2 cos (x) d x = 2 sin (x)

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

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

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

Vereinfache

= 2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= 2 sin (x) + 3 cos (x) + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

derivative f(x)=(6x+7)(7x-8)

d er i v a t i v e f (x) = (6 x + 7) (7 x - 8)

integral of 10sin(5x)

\int 10 sin (5 x) d x

integral of (1+2x^2)^2

\int (1 + 2 x^{2})^{2} d x

(dy)/(dx)=(2x)/(1+2y),y(2)=1

\frac{d y}{d x} = \frac{2 x}{1 + 2 y}, y (2) = 1

(2x)/y dx-(x^2)/(y^2)dy=0

\frac{2 x}{y} d x - \frac{x ^{2}}{y ^{2}} d y = 0