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Beliebt Rechnen >

integral of ln(x)+sin(pix)

Lösung

\int ln (x) + sin (π x) d x

Lösung

x ln (x) - x - \frac{1}{π} cos (π x) + C

Schritte zur Lösung

\int ln (x) + sin (π x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int ln (x) d x + \int sin (π x) d x

\int ln (x) d x = x ln (x) - x

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

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

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x - \frac{1}{π} cos (π x) + C

Graph

Beliebte Beispiele

integral of sin(x)-5cos(x)

\int sin (x) - 5 cos (x) d x

derivative sin((pix)^7)

d er i v a t i v e sin ((π x)^{7})

(\partial)/(\partial x)(9x+2y)

\frac{\partial}{\partial x} (9 x + 2 y)

fläche y=8x-12,y=x^2,x=1

a re a y = 8 x - 12, y = x^{2}, x = 1

limit as x approaches 0 of (tan(x))/(2x)

x \to 0 lim (\frac{tan ( x )}{2 x})