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Beliebt Rechnen >

integral of (ln(x)+cos(x))

Lösung

\int (ln (x) + cos (x)) d x

Lösung

x ln (x) - x + sin (x) + C

Schritte zur Lösung

\int ln (x) + cos (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 cos (x) d x

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

\int cos (x) d x = sin (x)

= x ln (x) - x + sin (x)

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x + sin (x) + C

Graph

Beliebte Beispiele

integral of sqrt(x)+3x

\int x + 3 x d x

integral of (5x^2-8x+5)

\int (5 x^{2} - 8 x + 5) d x

integral of 5arctan(4x)

\int 5 arctan (4 x) d x

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

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

integral of (e^{ax}+e^{-ax})^2

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