What is the integral of (x^2+2x)^{11}(2x+2) ?

The integral of (x^2+2x)^{11}(2x+2) is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x^2+2x)^{11}(2x+2)

\int (x^{2} + 2 x)^{11} (2 x + 2) d x

\frac{x ^{24}}{12} + 2 x^{23} + 22 x^{22} + \frac{440 x ^{21}}{3} + 660 x^{20} + 2112 x^{19} + 4928 x^{18} + 8448 x^{17} + 10560 x^{16} + \frac{28160 x ^{15}}{3} + 5632 x^{14} + 2048 x^{13} + \frac{1024 x ^{12}}{3} + C

Solution steps

\int (x^{2} + 2 x)^{11} (2 x + 2) d x

Expand

(x^{2} + 2 x)^{11} (2 x + 2) : 2 x^{23} + 46 x^{22} + 484 x^{21} + 3080 x^{20} + 13200 x^{19} + 40128 x^{18} + 88704 x^{17} + 143616 x^{16} + 168960 x^{15} + 140800 x^{14} + 78848 x^{13} + 26624 x^{12} + 4096 x^{11}

= \int 2 x^{23} + 46 x^{22} + 484 x^{21} + 3080 x^{20} + 13200 x^{19} + 40128 x^{18} + 88704 x^{17} + 143616 x^{16} + 168960 x^{15} + 140800 x^{14} + 78848 x^{13} + 26624 x^{12} + 4096 x^{11} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 x^{23} d x + \int 46 x^{22} d x + \int 484 x^{21} d x + \int 3080 x^{20} d x + \int 13200 x^{19} d x + \int 40128 x^{18} d x + \int 88704 x^{17} d x + \int 143616 x^{16} d x + \int 168960 x^{15} d x + \int 140800 x^{14} d x + \int 78848 x^{13} d x + \int 26624 x^{12} d x + \int 4096 x^{11} d x

\int 2 x^{23} d x = \frac{x ^{24}}{12}

\int 46 x^{22} d x = 2 x^{23}

\int 484 x^{21} d x = 22 x^{22}

\int 3080 x^{20} d x = \frac{440 x ^{21}}{3}

\int 13200 x^{19} d x = 660 x^{20}

\int 40128 x^{18} d x = 2112 x^{19}

\int 88704 x^{17} d x = 4928 x^{18}

\int 143616 x^{16} d x = 8448 x^{17}

\int 168960 x^{15} d x = 10560 x^{16}

\int 140800 x^{14} d x = \frac{28160 x ^{15}}{3}

\int 78848 x^{13} d x = 5632 x^{14}

\int 26624 x^{12} d x = 2048 x^{13}

\int 4096 x^{11} d x = \frac{1024 x ^{12}}{3}

= \frac{x ^{24}}{12} + 2 x^{23} + 22 x^{22} + \frac{440 x ^{21}}{3} + 660 x^{20} + 2112 x^{19} + 4928 x^{18} + 8448 x^{17} + 10560 x^{16} + \frac{28160 x ^{15}}{3} + 5632 x^{14} + 2048 x^{13} + \frac{1024 x ^{12}}{3}

Add a constant to the solution

= \frac{x ^{24}}{12} + 2 x^{23} + 22 x^{22} + \frac{440 x ^{21}}{3} + 660 x^{20} + 2112 x^{19} + 4928 x^{18} + 8448 x^{17} + 10560 x^{16} + \frac{28160 x ^{15}}{3} + 5632 x^{14} + 2048 x^{13} + \frac{1024 x ^{12}}{3} + C

\int \frac{100 t}{t ^{2} + 2} d t

\int (x) ln (x) d x

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

\int x^{2} e^{- 2 a x} d x

\int sin (4 x - 9) d x

What is the integral of (x^2+2x)^{11}(2x+2) ?
The integral of (x^2+2x)^{11}(2x+2) is