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Beliebt Rechnen >

integral of sin(x)x^3

Lösung

\int sin (x) x^{3} d x

Lösung

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

Schritte zur Lösung

\int sin (x) x^{3} d x

Wende die partielle Integration an

= - x^{3} cos (x) - \int - 3 x^{2} cos (x) d x

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (sin^5(5x)+cos^3(5x))

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

integral of (7/5)^x

\int (\frac{7}{5})^{x} d x

integral of-5x^{-2}

\int - 5 x^{- 2} d x

integral of 8xsqrt(x)

\int 8 x x d x

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

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