integral of 4+10(x+5)^{-2}

Lösung

\int 4 + 10 (x + 5)^{- 2} d x

4 x - \frac{10}{x + 5} + C

Schritte zur Lösung

\int 4 + 10 (x + 5)^{- 2} d x

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

= \int 4 + \frac{10}{( x + 5 ) ^{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 4 d x + \int \frac{10}{( x + 5 ) ^{2}} d x

\int 4 d x = 4 x

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

= 4 x - \frac{10}{x + 5}

Füge eine Konstante zur Lösung hinzu

= 4 x - \frac{10}{x + 5} + C

\int 4 x + 9 d x

\int \frac{5 x ^{4}}{( x ^{5} + 1 ) ^{2}} d x

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\int (sin (x))^{5} (cos (x))^{6} d x