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Beliebt Rechnen >

integral of (rivative of 4x)/((x^2-9))

Lösung

\int \frac{\frac{d}{d x} ( 4 x )}{( x ^{2} - 9 )} d x

Lösung

\frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9} + C

Schritte zur Lösung

\int \frac{\frac{d}{d x} ( 4 x )}{x ^{2} - 9} d x

Wende die partielle Integration an

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \int - \frac{8 x}{( x ^{2} - 9 ) ^{2}} d x

\int - \frac{8 x}{( x ^{2} - 9 ) ^{2}} d x = \frac{4}{x ^{2} - 9}

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9}

Füge eine Konstante zur Lösung hinzu

= \frac{x \frac{d}{d x} ( 4 x )}{x ^{2} - 9} - \frac{4}{x ^{2} - 9} + C

Graph

Beliebte Beispiele

integral of (x^2ln^3(2+x^3))/(2+x^3)

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

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

\int \frac{x ^{2} - 3 x - 5}{x - 2} d x

integral of 1/2 x3^x

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

integral of 1/(4x^2-16x+17)

\int \frac{1}{4 x ^{2} - 16 x + 17} d x

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

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