de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x^2(7x^3-3)^5

Lösung

\int x^{2} (7 x^{3} - 3)^{5} d x

Lösung

\frac{16807 x ^{18}}{18} - 2401 x^{15} + \frac{5145 x ^{12}}{2} - 1470 x^{9} + \frac{945 x ^{6}}{2} - 81 x^{3} + C

Schritte zur Lösung

\int x^{2} (7 x^{3} - 3)^{5} d x

Multipliziere aus

x^{2} (7 x^{3} - 3)^{5} : 16807 x^{17} - 36015 x^{14} + 30870 x^{11} - 13230 x^{8} + 2835 x^{5} - 243 x^{2}

= \int 16807 x^{17} - 36015 x^{14} + 30870 x^{11} - 13230 x^{8} + 2835 x^{5} - 243 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

= \int 16807 x^{17} d x - \int 36015 x^{14} d x + \int 30870 x^{11} d x - \int 13230 x^{8} d x + \int 2835 x^{5} d x - \int 243 x^{2} d x

\int 16807 x^{17} d x = \frac{16807 x ^{18}}{18}

\int 36015 x^{14} d x = 2401 x^{15}

\int 30870 x^{11} d x = \frac{5145 x ^{12}}{2}

\int 13230 x^{8} d x = 1470 x^{9}

\int 2835 x^{5} d x = \frac{945 x ^{6}}{2}

\int 243 x^{2} d x = 81 x^{3}

= \frac{16807 x ^{18}}{18} - 2401 x^{15} + \frac{5145 x ^{12}}{2} - 1470 x^{9} + \frac{945 x ^{6}}{2} - 81 x^{3}

Füge eine Konstante zur Lösung hinzu

= \frac{16807 x ^{18}}{18} - 2401 x^{15} + \frac{5145 x ^{12}}{2} - 1470 x^{9} + \frac{945 x ^{6}}{2} - 81 x^{3} + C

Graph

Beliebte Beispiele

integral of (x^3+2x)(x^4+4x^2+4)^7

\int (x^{3} + 2 x) (x^{4} + 4 x^{2} + 4)^{7} d x

integral of (1-cos(2u))/2

\int \frac{1 - cos ( 2 u )}{2} d u

integral of ((-5x+15))/((x^2+2x+4)^2)

\int \frac{( - 5 x + 15 )}{( x ^{2} + 2 x + 4 ) ^{2}} d x

integral of 1/((x-1)sqrt(x))

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

integral of x/(sec(2x))

\int \frac{x}{sec ( 2 x )} d x