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Beliebt Rechnen >

integral of 2(sin(x)-cos(x)+1)

Lösung

\int 2 (sin (x) - cos (x) + 1) d x

Lösung

2 (- cos (x) - sin (x) + x) + C

Schritte zur Lösung

\int 2 (sin (x) - cos (x) + 1) d x

Entferne die Konstante:

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

= 2 \cdot \int sin (x) - cos (x) + 1 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

= 2 (\int sin (x) d x - \int cos (x) d x + \int 1 d x)

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

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

\int 1 d x = x

= 2 (- cos (x) - sin (x) + x)

Füge eine Konstante zur Lösung hinzu

= 2 (- cos (x) - sin (x) + x) + C

Graph

Beliebte Beispiele

(dy)/(dt)+y=cos(2t),y(0)=5

\frac{d y}{d t} + y = cos (2 t), y (0) = 5

(dy)/(dx)= 1/(xy)

\frac{d y}{d x} = \frac{1}{x y}

derivative f(x)=xsqrt(x^3-6)

d er i v a t i v e f (x) = x x^{3} - 6

derivative y=2x^2sqrt(2-x)

d er i v a t i v e y = 2 x^{2} 2 - x

(\partial)/(\partial x)(e^{-1}cos(pix))

\frac{\partial}{\partial x} (e^{- 1} cos (π x))