integral of x^2sin(7x)

Lösung

\int x^{2} sin (7 x) d x

- \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)) + C

Schritte zur Lösung

\int x^{2} sin (7 x) d x

Wende die partielle Integration an

= - \frac{1}{7} x^{2} cos (7 x) - \int - \frac{2}{7} x cos (7 x) d x

\int - \frac{2}{7} x cos (7 x) d x = - \frac{2}{343} (7 x sin (7 x) + cos (7 x))

= - \frac{1}{7} x^{2} cos (7 x) - (- \frac{2}{343} (7 x sin (7 x) + cos (7 x)))

Vereinfache

= - \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x))

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{7} x^{2} cos (7 x) + \frac{2}{343} (7 x sin (7 x) + cos (7 x)) + C

d er i v a t i v e \frac{z}{1 + z ^{2}}

\int (\frac{1}{( 2 x - 3 ) ( 3 x ^{2} + x )}) d x

\frac{\partial}{\partial t} (t^{6} e^{- x})

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y^{^{'}} \cdot cos (t) + y \cdot sin (t) = tan (t)