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Beliebt Rechnen >

integral of (x^2*sin(x))

Lösung

\int (x^{2} \cdot sin (x)) d x

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

= - 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

derivative of x^{2/3}+y^{2/3}

\frac{d}{d x} (x^{\frac{2}{3}} + y^{\frac{2}{3}})

derivative of-tan(x^2)

\frac{d}{d x} (- tan (x^{2}))

integral of 1/(ln(x^2))

\int \frac{1}{ln ( x ^{2} )} d x

sum from n=1 to infinity of (3^n)/(5^n)

n = 1 \sum \infty \frac{3 ^{n}}{5 ^{n}}

limit as x approaches 0 of (9+x)/(x^3)

x \to 0 lim (\frac{9 + x}{x ^{3}})