de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{33}}{11} + 4 x^{30} + 80 x^{27} + 960 x^{24} + 7680 x^{21} + 43008 x^{18} + 172032 x^{15} + 491520 x^{12} + 983040 x^{9} + 1310720 x^{6} + 1048576 x^{3} + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int x^{2} (x^{3} + 4)^{10} d x

Multipliziere aus

x^{2} (x^{3} + 4)^{10} : x^{32} + 40 x^{29} + 720 x^{26} + 7680 x^{23} + 53760 x^{20} + 258048 x^{17} + 860160 x^{14} + 1966080 x^{11} + 2949120 x^{8} + 2621440 x^{5} + 1048576 x^{2}

= 3 \cdot \int x^{32} + 40 x^{29} + 720 x^{26} + 7680 x^{23} + 53760 x^{20} + 258048 x^{17} + 860160 x^{14} + 1966080 x^{11} + 2949120 x^{8} + 2621440 x^{5} + 1048576 x^{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

= 3 (\int x^{32} d x + \int 40 x^{29} d x + \int 720 x^{26} d x + \int 7680 x^{23} d x + \int 53760 x^{20} d x + \int 258048 x^{17} d x + \int 860160 x^{14} d x + \int 1966080 x^{11} d x + \int 2949120 x^{8} d x + \int 2621440 x^{5} d x + \int 1048576 x^{2} d x)

\int x^{32} d x = \frac{x ^{33}}{33}

\int 40 x^{29} d x = \frac{4 x ^{30}}{3}

\int 720 x^{26} d x = \frac{80 x ^{27}}{3}

\int 7680 x^{23} d x = 320 x^{24}

\int 53760 x^{20} d x = 2560 x^{21}

\int 258048 x^{17} d x = 14336 x^{18}

\int 860160 x^{14} d x = 57344 x^{15}

\int 1966080 x^{11} d x = 163840 x^{12}

\int 2949120 x^{8} d x = 327680 x^{9}

\int 2621440 x^{5} d x = \frac{1310720 x ^{6}}{3}

\int 1048576 x^{2} d x = \frac{1048576 x ^{3}}{3}

= 3 (\frac{x ^{33}}{33} + \frac{4 x ^{30}}{3} + \frac{80 x ^{27}}{3} + 320 x^{24} + 2560 x^{21} + 14336 x^{18} + 57344 x^{15} + 163840 x^{12} + 327680 x^{9} + \frac{1310720 x ^{6}}{3} + \frac{1048576 x ^{3}}{3})

Vereinfache

3 (\frac{x ^{33}}{33} + \frac{4 x ^{30}}{3} + \frac{80 x ^{27}}{3} + 320 x^{24} + 2560 x^{21} + 14336 x^{18} + 57344 x^{15} + 163840 x^{12} + 327680 x^{9} + \frac{1310720 x ^{6}}{3} + \frac{1048576 x ^{3}}{3}) : \frac{x ^{33}}{11} + 4 x^{30} + 80 x^{27} + 960 x^{24} + 7680 x^{21} + 43008 x^{18} + 172032 x^{15} + 491520 x^{12} + 983040 x^{9} + 1310720 x^{6} + 1048576 x^{3}

= \frac{x ^{33}}{11} + 4 x^{30} + 80 x^{27} + 960 x^{24} + 7680 x^{21} + 43008 x^{18} + 172032 x^{15} + 491520 x^{12} + 983040 x^{9} + 1310720 x^{6} + 1048576 x^{3}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{33}}{11} + 4 x^{30} + 80 x^{27} + 960 x^{24} + 7680 x^{21} + 43008 x^{18} + 172032 x^{15} + 491520 x^{12} + 983040 x^{9} + 1310720 x^{6} + 1048576 x^{3} + C

Graph

Beliebte Beispiele

derivative of (5x/(1-x))

\frac{d}{d x} (\frac{5 x}{1 - x})

derivative of 2xsin(2x)

\frac{d}{d x} (2 x sin (2 x))

y^{''}+2y^'+10y=cos(t)+0.739

y^{^{''}} + 2 y^{^{'}} + 10 y = cos (t) + 0.739

derivative f(x)=11x^3tan(x)

d er i v a t i v e f (x) = 11 x^{3} tan (x)

derivative of (6x^2-12x+12e^x)

\frac{d}{d x} ((6 x^{2} - 12 x + 12) e^{x})