integral of 10-x/((x^2+1)^2)

Lösung

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

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

Schritte zur Lösung

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

\int 10 d x = 10 x

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

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