integral of (3x-sqrt(2))^5

Lösung

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

\frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x + C

Schritte zur Lösung

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

Multipliziere aus

(3 x - 2)^{5} : 243 x^{5} - 4052 x^{4} + 540 x^{3} - 90 \cdot 2^{\frac{3}{2}} x^{2} + 60 x - 2^{\frac{5}{2}}

= \int 243 x^{5} - 4052 x^{4} + 540 x^{3} - 90 \cdot 2^{\frac{3}{2}} x^{2} + 60 x - 2^{\frac{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 243 x^{5} d x - \int 4052 x^{4} d x + \int 540 x^{3} d x - \int 90 \cdot 2^{\frac{3}{2}} x^{2} d x + \int 60 x d x - \int 2^{\frac{5}{2}} d x

\int 243 x^{5} d x = \frac{81 x ^{6}}{2}

\int 4052 x^{4} d x = 812 x^{5}

\int 540 x^{3} d x = 135 x^{4}

\int 90 \cdot 2^{\frac{3}{2}} x^{2} d x = 602 x^{3}

\int 60 x d x = 30 x^{2}

\int 2^{\frac{5}{2}} d x = 42 x

= \frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x

Füge eine Konstante zur Lösung hinzu

= \frac{81 x ^{6}}{2} - 812 x^{5} + 135 x^{4} - 602 x^{3} + 30 x^{2} - 42 x + C

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