integral of-3x^{-5}+7x^2-6x+3

Lösung

\int - 3 x^{- 5} + 7 x^{2} - 6 x + 3 d x

\frac{3}{4 x ^{4}} + \frac{7 x ^{3}}{3} - 3 x^{2} + 3 x + C

Schritte zur Lösung

\int - 3 x^{- 5} + 7 x^{2} - 6 x + 3 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 3 x^{- 5} d x + \int 7 x^{2} d x - \int 6 x d x + \int 3 d x

\int 3 x^{- 5} d x = - \frac{3}{4 x ^{4}}

\int 7 x^{2} d x = \frac{7 x ^{3}}{3}

\int 6 x d x = 3 x^{2}

\int 3 d x = 3 x

= - (- \frac{3}{4 x ^{4}}) + \frac{7 x ^{3}}{3} - 3 x^{2} + 3 x

Vereinfache

= \frac{3}{4 x ^{4}} + \frac{7 x ^{3}}{3} - 3 x^{2} + 3 x

Füge eine Konstante zur Lösung hinzu

= \frac{3}{4 x ^{4}} + \frac{7 x ^{3}}{3} - 3 x^{2} + 3 x + C

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