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Beliebt Rechnen >

integral of x^3+1/x-7

Lösung

\int x^{3} + \frac{1}{x} - 7 d x

Lösung

\frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x + C

Schritte zur Lösung

\int x^{3} + \frac{1}{x} - 7 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 x^{3} d x + \int \frac{1}{x} d x - \int 7 d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{1}{x} d x = ln ∣ x ∣

\int 7 d x = 7 x

= \frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{4}}{4} + ln ∣ x ∣ - 7 x + C

Graph

Beliebte Beispiele

integral of (2^x)/(sqrt(1+4^x))

\int \frac{2 ^{x}}{1 + 4 ^{x}} d x

integral of (1+t^2)^{1/2}

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

integral of (e^x)/((e^{2x)+1)(e^x-3)}

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

integral of-x^2-2

\int - x^{2} - 2 d x

integral of arctan(sqrt(x-1))

\int arctan (x - 1) d x