integral x/((5x+2)^3)

Lösung

integral

\frac{x}{( 5 x + 2 ) ^{3}}

- \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x

\int - \frac{1}{10 ( 5 x + 2 ) ^{2}} d x = \frac{1}{50 ( 5 x + 2 )}

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )}

Füge eine Konstante zur Lösung hinzu

= - \frac{x}{10 ( 5 x + 2 ) ^{2}} - \frac{1}{50 ( 5 x + 2 )} + C

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