integral of (5x-3)^2

Lösung

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

\frac{25 x ^{3}}{3} - 15 x^{2} + 9 x + C

Schritte zur Lösung

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

Multipliziere aus

(5 x - 3)^{2} : 25 x^{2} - 30 x + 9

= \int 25 x^{2} - 30 x + 9 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 25 x^{2} d x - \int 30 x d x + \int 9 d x

\int 25 x^{2} d x = \frac{25 x ^{3}}{3}

\int 30 x d x = 15 x^{2}

\int 9 d x = 9 x

= \frac{25 x ^{3}}{3} - 15 x^{2} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{25 x ^{3}}{3} - 15 x^{2} + 9 x + C

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

\int (3 - 4 x) d x

\int \frac{x ^{2} + 2 x - 1}{x ^{3} - 27} d x

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\int \frac{2 x - 1}{x} d x