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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

= - cos (x) (x^{2} + 1) - (- 2 (x sin (x) + cos (x)))

Vereinfache

- cos (x) (x^{2} + 1) - (- 2 (x sin (x) + cos (x))) : - x^{2} cos (x) + 2 x sin (x) + cos (x)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x\sqrt[3]{x+4}

\int x 3 x + 4 d x

integral from 1 to 3 of xsqrt(x^2+1)

\int_{1}^{3} x x^{2} + 1 d x

\frac{d}{d y} (3)

derivative of xsqrt(5-x)

\frac{d}{d x} (x 5 - x)

derivative (cos(t))/t

d er i v a t i v e \frac{cos ( t )}{t}