integral of (x^{10}-x^5+4)^3(2x^9-x^4)

Lösung

\int (x^{10} - x^{5} + 4)^{3} (2 x^{9} - x^{4}) d x

\frac{x ^{40}}{20} - \frac{x ^{35}}{5} + \frac{11 x ^{30}}{10} - \frac{13 x ^{25}}{5} + \frac{29 x ^{20}}{4} - \frac{52 x ^{15}}{5} + \frac{88 x ^{10}}{5} - \frac{64 x ^{5}}{5} + C

Schritte zur Lösung

\int (x^{10} - x^{5} + 4)^{3} (2 x^{9} - x^{4}) d x

Multipliziere aus

(x^{10} - x^{5} + 4)^{3} (2 x^{9} - x^{4}) : 2 x^{39} - 7 x^{34} + 33 x^{29} - 65 x^{24} + 145 x^{19} - 156 x^{14} + 176 x^{9} - 64 x^{4}

= \int 2 x^{39} - 7 x^{34} + 33 x^{29} - 65 x^{24} + 145 x^{19} - 156 x^{14} + 176 x^{9} - 64 x^{4} 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 2 x^{39} d x - \int 7 x^{34} d x + \int 33 x^{29} d x - \int 65 x^{24} d x + \int 145 x^{19} d x - \int 156 x^{14} d x + \int 176 x^{9} d x - \int 64 x^{4} d x

\int 2 x^{39} d x = \frac{x ^{40}}{20}

\int 7 x^{34} d x = \frac{x ^{35}}{5}

\int 33 x^{29} d x = \frac{11 x ^{30}}{10}

\int 65 x^{24} d x = \frac{13 x ^{25}}{5}

\int 145 x^{19} d x = \frac{29 x ^{20}}{4}

\int 156 x^{14} d x = \frac{52 x ^{15}}{5}

\int 176 x^{9} d x = \frac{88 x ^{10}}{5}

\int 64 x^{4} d x = \frac{64 x ^{5}}{5}

= \frac{x ^{40}}{20} - \frac{x ^{35}}{5} + \frac{11 x ^{30}}{10} - \frac{13 x ^{25}}{5} + \frac{29 x ^{20}}{4} - \frac{52 x ^{15}}{5} + \frac{88 x ^{10}}{5} - \frac{64 x ^{5}}{5}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{40}}{20} - \frac{x ^{35}}{5} + \frac{11 x ^{30}}{10} - \frac{13 x ^{25}}{5} + \frac{29 x ^{20}}{4} - \frac{52 x ^{15}}{5} + \frac{88 x ^{10}}{5} - \frac{64 x ^{5}}{5} + C

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