What is the integral of x^7(x-2)^4(x-3)^9 ?

The integral of x^7(x-2)^4(x-3)^9 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^7(x-2)^4(x-3)^9

\int x^{7} (x - 2)^{4} (x - 3)^{9} d x

\frac{x ^{21}}{21} - \frac{7 x ^{20}}{4} + \frac{564 x ^{19}}{19} - \frac{2770 x ^{18}}{9} + \frac{37006 x ^{17}}{17} - \frac{88749 x ^{16}}{8} + \frac{209628 x ^{15}}{5} - \frac{833166 x ^{14}}{7} + \frac{3301641 x ^{13}}{13} - \frac{1610361 x ^{12}}{4} + \frac{5073840 x ^{11}}{11} - \frac{1810836 x ^{10}}{5} + 174960 x^{9} - 39366 x^{8} + C

Solution steps

\int x^{7} (x - 2)^{4} (x - 3)^{9} d x

Expand

x^{7} (x - 2)^{4} (x - 3)^{9} : x^{20} - 35 x^{19} + 564 x^{18} - 5540 x^{17} + 37006 x^{16} - 177498 x^{15} + 628884 x^{14} - 1666332 x^{13} + 3301641 x^{12} - 4831083 x^{11} + 5073840 x^{10} - 3621672 x^{9} + 1574640 x^{8} - 314928 x^{7}

= \int x^{20} - 35 x^{19} + 564 x^{18} - 5540 x^{17} + 37006 x^{16} - 177498 x^{15} + 628884 x^{14} - 1666332 x^{13} + 3301641 x^{12} - 4831083 x^{11} + 5073840 x^{10} - 3621672 x^{9} + 1574640 x^{8} - 314928 x^{7} 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 x^{20} d x - \int 35 x^{19} d x + \int 564 x^{18} d x - \int 5540 x^{17} d x + \int 37006 x^{16} d x - \int 177498 x^{15} d x + \int 628884 x^{14} d x - \int 1666332 x^{13} d x + \int 3301641 x^{12} d x - \int 4831083 x^{11} d x + \int 5073840 x^{10} d x - \int 3621672 x^{9} d x + \int 1574640 x^{8} d x - \int 314928 x^{7} d x

\int x^{20} d x = \frac{x ^{21}}{21}

\int 35 x^{19} d x = \frac{7 x ^{20}}{4}

\int 564 x^{18} d x = \frac{564 x ^{19}}{19}

\int 5540 x^{17} d x = \frac{2770 x ^{18}}{9}

\int 37006 x^{16} d x = \frac{37006 x ^{17}}{17}

\int 177498 x^{15} d x = \frac{88749 x ^{16}}{8}

\int 628884 x^{14} d x = \frac{209628 x ^{15}}{5}

\int 1666332 x^{13} d x = \frac{833166 x ^{14}}{7}

\int 3301641 x^{12} d x = \frac{3301641 x ^{13}}{13}

\int 4831083 x^{11} d x = \frac{1610361 x ^{12}}{4}

\int 5073840 x^{10} d x = \frac{5073840 x ^{11}}{11}

\int 3621672 x^{9} d x = \frac{1810836 x ^{10}}{5}

\int 1574640 x^{8} d x = 174960 x^{9}

\int 314928 x^{7} d x = 39366 x^{8}

= \frac{x ^{21}}{21} - \frac{7 x ^{20}}{4} + \frac{564 x ^{19}}{19} - \frac{2770 x ^{18}}{9} + \frac{37006 x ^{17}}{17} - \frac{88749 x ^{16}}{8} + \frac{209628 x ^{15}}{5} - \frac{833166 x ^{14}}{7} + \frac{3301641 x ^{13}}{13} - \frac{1610361 x ^{12}}{4} + \frac{5073840 x ^{11}}{11} - \frac{1810836 x ^{10}}{5} + 174960 x^{9} - 39366 x^{8}

Add a constant to the solution

= \frac{x ^{21}}{21} - \frac{7 x ^{20}}{4} + \frac{564 x ^{19}}{19} - \frac{2770 x ^{18}}{9} + \frac{37006 x ^{17}}{17} - \frac{88749 x ^{16}}{8} + \frac{209628 x ^{15}}{5} - \frac{833166 x ^{14}}{7} + \frac{3301641 x ^{13}}{13} - \frac{1610361 x ^{12}}{4} + \frac{5073840 x ^{11}}{11} - \frac{1810836 x ^{10}}{5} + 174960 x^{9} - 39366 x^{8} + C

\int \frac{4}{t ^{3}} d t

\int tan (x) d tan (x) d x

\int (\frac{x ^{2} + x + 1}{x}) d x

\int x^{2} + 2 x + 2 d x

\int \frac{4}{( 4 x - 1 ) ln ( 4 x - 1 )} d x

What is the integral of x^7(x-2)^4(x-3)^9 ?
The integral of x^7(x-2)^4(x-3)^9 is