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Beliebt Rechnen >

integral of ax^3+6/(x^2)

Lösung

\int a x^{3} + \frac{6}{x ^{2}} d x

Lösung

\frac{a x ^{4}}{4} - \frac{6}{x} + C

Schritte zur Lösung

\int a x^{3} + \frac{6}{x ^{2}} 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 a x^{3} d x + \int \frac{6}{x ^{2}} d x

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

\int \frac{6}{x ^{2}} d x = - \frac{6}{x}

= \frac{a x ^{4}}{4} - \frac{6}{x}

Füge eine Konstante zur Lösung hinzu

= \frac{a x ^{4}}{4} - \frac{6}{x} + C

Graph

Beliebte Beispiele

integral of (cos^4(x))/(sin^4(x))

\int \frac{cos ^{4} ( x )}{sin ^{4} ( x )} d x

integral of (3x^2-5x+3)

\int (3 x^{2} - 5 x + 3) d x

integral of 1/(sqrt(x^2-8x-9))

\int \frac{1}{x ^{2} - 8 x - 9} d x

integral of 3x^{1/2}+3

\int 3 x^{\frac{1}{2}} + 3 d x

integral of (x^6)/((3+x^7)^2)

\int \frac{x ^{6}}{( 3 + x ^{7} ) ^{2}} d x