integral of (x-1)sin(pix)

Lösung

\int (x - 1) sin (π x) d x

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

Schritte zur Lösung

\int (x - 1) sin (π x) d x

Wende die partielle Integration an

= - \frac{1}{π} cos (π x) (x - 1) - \int - \frac{1}{π} cos (π x) d x

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

= - \frac{1}{π} cos (π x) (x - 1) - (- \frac{1}{π ^{2}} sin (π x))

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int x^{3} sin (x^{4}) d x

\int 9 x^{5} e^{8 x^{2}} d x

\frac{\partial}{\partial y} (x^{3} y^{2})

\int cos (3 θ) d θ

x \to - 2 lim (\frac{3 x - 6}{x + 2})