What is the integral of x^{19}(x^{20}-3)^{10} ?

The integral of x^{19}(x^{20}-3)^{10} is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of x^{19}(x^{20}-3)^{10}

\int x^{19} (x^{20} - 3)^{10} d x

\frac{x ^{220}}{220} - \frac{3 x ^{200}}{20} + \frac{9 x ^{180}}{4} - \frac{81 x ^{160}}{4} + \frac{243 x ^{140}}{2} - \frac{5103 x ^{120}}{10} + \frac{15309 x ^{100}}{10} - \frac{6561 x ^{80}}{2} + \frac{19683 x ^{60}}{4} - \frac{19683 x ^{40}}{4} + \frac{59049 x ^{20}}{20} + C

Solution steps

\int x^{19} (x^{20} - 3)^{10} d x

Expand

x^{19} (x^{20} - 3)^{10} : x^{219} - 30 x^{199} + 405 x^{179} - 3240 x^{159} + 17010 x^{139} - 61236 x^{119} + 153090 x^{99} - 262440 x^{79} + 295245 x^{59} - 196830 x^{39} + 59049 x^{19}

= \int x^{219} - 30 x^{199} + 405 x^{179} - 3240 x^{159} + 17010 x^{139} - 61236 x^{119} + 153090 x^{99} - 262440 x^{79} + 295245 x^{59} - 196830 x^{39} + 59049 x^{19} 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^{219} d x - \int 30 x^{199} d x + \int 405 x^{179} d x - \int 3240 x^{159} d x + \int 17010 x^{139} d x - \int 61236 x^{119} d x + \int 153090 x^{99} d x - \int 262440 x^{79} d x + \int 295245 x^{59} d x - \int 196830 x^{39} d x + \int 59049 x^{19} d x

\int x^{219} d x = \frac{x ^{220}}{220}

\int 30 x^{199} d x = \frac{3 x ^{200}}{20}

\int 405 x^{179} d x = \frac{9 x ^{180}}{4}

\int 3240 x^{159} d x = \frac{81 x ^{160}}{4}

\int 17010 x^{139} d x = \frac{243 x ^{140}}{2}

\int 61236 x^{119} d x = \frac{5103 x ^{120}}{10}

\int 153090 x^{99} d x = \frac{15309 x ^{100}}{10}

\int 262440 x^{79} d x = \frac{6561 x ^{80}}{2}

\int 295245 x^{59} d x = \frac{19683 x ^{60}}{4}

\int 196830 x^{39} d x = \frac{19683 x ^{40}}{4}

\int 59049 x^{19} d x = \frac{59049 x ^{20}}{20}

= \frac{x ^{220}}{220} - \frac{3 x ^{200}}{20} + \frac{9 x ^{180}}{4} - \frac{81 x ^{160}}{4} + \frac{243 x ^{140}}{2} - \frac{5103 x ^{120}}{10} + \frac{15309 x ^{100}}{10} - \frac{6561 x ^{80}}{2} + \frac{19683 x ^{60}}{4} - \frac{19683 x ^{40}}{4} + \frac{59049 x ^{20}}{20}

Add a constant to the solution

= \frac{x ^{220}}{220} - \frac{3 x ^{200}}{20} + \frac{9 x ^{180}}{4} - \frac{81 x ^{160}}{4} + \frac{243 x ^{140}}{2} - \frac{5103 x ^{120}}{10} + \frac{15309 x ^{100}}{10} - \frac{6561 x ^{80}}{2} + \frac{19683 x ^{60}}{4} - \frac{19683 x ^{40}}{4} + \frac{59049 x ^{20}}{20} + C

\int \frac{x - 3}{x + 3} d x

\int \frac{x ^{2} - x - 2}{x ^{4} + x ^{2}} d x

\int arcsin (2 x + 1) d x

\int csc (4 x + 1) cot (4 x + 1) d x

\int \frac{4 cos ( 2 x )}{3 - sin ( 2 x )} d x

What is the integral of x^{19}(x^{20}-3)^{10} ?
The integral of x^{19}(x^{20}-3)^{10} is