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Beliebt Rechnen >

integral of (6e^{5x}-7/x)

Lösung

\int (6 e^{5 x} - \frac{7}{x}) d x

Lösung

\frac{6}{5} e^{5 x} - 7 ln ∣ x ∣ + C

Schritte zur Lösung

\int 6 e^{5 x} - \frac{7}{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 6 e^{5 x} d x - \int \frac{7}{x} d x

\int 6 e^{5 x} d x = \frac{6}{5} e^{5 x}

\int \frac{7}{x} d x = 7 ln ∣ x ∣

= \frac{6}{5} e^{5 x} - 7 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{6}{5} e^{5 x} - 7 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

derivative of (6x-3/(x-3))

\frac{d}{d x} (\frac{6 x - 3}{x - 3})

integral of sin(6t)

\int sin (6 t) d t

derivative of (sin(0.5sqrt(x))/x)

\frac{d}{d x} (\frac{sin ( 0.5 x )}{x})

integral of-(2000x)/((1+x^2))

\int - \frac{2000 x}{( 1 + x ^{2} )} d x

tangent x^2,\at x=2

t an g e n t x^{2}, at x = 2