en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-4)^{13}

Solution

\int (2 x - 4)^{13} d x

Solution

\frac{4096 x ^{14}}{7} - 16384 x^{13} + 212992 x^{12} - 1703936 x^{11} + 9371648 x^{10} - 37486592 x^{9} + 112459776 x^{8} - \frac{1799356416 x ^{7}}{7} + 449839104 x^{6} - 599785472 x^{5} + 599785472 x^{4} - 436207616 x^{3} + 218103808 x^{2} - 67108864 x + C

Solution steps

\int (2 x - 4)^{13} d x

Expand

(2 x - 4)^{13} : 8192 x^{13} - 212992 x^{12} + 2555904 x^{11} - 18743296 x^{10} + 93716480 x^{9} - 337379328 x^{8} + 899678208 x^{7} - 1799356416 x^{6} + 2699034624 x^{5} - 2998927360 x^{4} + 2399141888 x^{3} - 1308622848 x^{2} + 436207616 x - 67108864

= \int 8192 x^{13} - 212992 x^{12} + 2555904 x^{11} - 18743296 x^{10} + 93716480 x^{9} - 337379328 x^{8} + 899678208 x^{7} - 1799356416 x^{6} + 2699034624 x^{5} - 2998927360 x^{4} + 2399141888 x^{3} - 1308622848 x^{2} + 436207616 x - 67108864 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 8192 x^{13} d x - \int 212992 x^{12} d x + \int 2555904 x^{11} d x - \int 18743296 x^{10} d x + \int 93716480 x^{9} d x - \int 337379328 x^{8} d x + \int 899678208 x^{7} d x - \int 1799356416 x^{6} d x + \int 2699034624 x^{5} d x - \int 2998927360 x^{4} d x + \int 2399141888 x^{3} d x - \int 1308622848 x^{2} d x + \int 436207616 x d x - \int 67108864 d x

\int 8192 x^{13} d x = \frac{4096 x ^{14}}{7}

\int 212992 x^{12} d x = 16384 x^{13}

\int 2555904 x^{11} d x = 212992 x^{12}

\int 18743296 x^{10} d x = 1703936 x^{11}

\int 93716480 x^{9} d x = 9371648 x^{10}

\int 337379328 x^{8} d x = 37486592 x^{9}

\int 899678208 x^{7} d x = 112459776 x^{8}

\int 1799356416 x^{6} d x = \frac{1799356416 x ^{7}}{7}

\int 2699034624 x^{5} d x = 449839104 x^{6}

\int 2998927360 x^{4} d x = 599785472 x^{5}

\int 2399141888 x^{3} d x = 599785472 x^{4}

\int 1308622848 x^{2} d x = 436207616 x^{3}

\int 436207616 x d x = 218103808 x^{2}

\int 67108864 d x = 67108864 x

= \frac{4096 x ^{14}}{7} - 16384 x^{13} + 212992 x^{12} - 1703936 x^{11} + 9371648 x^{10} - 37486592 x^{9} + 112459776 x^{8} - \frac{1799356416 x ^{7}}{7} + 449839104 x^{6} - 599785472 x^{5} + 599785472 x^{4} - 436207616 x^{3} + 218103808 x^{2} - 67108864 x

Add a constant to the solution

= \frac{4096 x ^{14}}{7} - 16384 x^{13} + 212992 x^{12} - 1703936 x^{11} + 9371648 x^{10} - 37486592 x^{9} + 112459776 x^{8} - \frac{1799356416 x ^{7}}{7} + 449839104 x^{6} - 599785472 x^{5} + 599785472 x^{4} - 436207616 x^{3} + 218103808 x^{2} - 67108864 x + C

Popular Examples

integral of-2e^{-2t}

\int - 2 e^{- 2 t} d t

integral of (cos(pi/(x^{45)}))/(x^{46)}

\int \frac{cos ( \frac{π}{x ^{45}} )}{x ^{46}} d x

integral of (6x^2-5x^4-2)/(sqrt(x))

\int \frac{6 x ^{2} - 5 x ^{4} - 2}{x} d x

integral of sin(2ln(x))

\int sin (2 ln (x)) d x

integral of (2x+1)cos(4x)

\int (2 x + 1) cos (4 x) d x

Frequently Asked Questions (FAQ)

What is the integral of (2x-4)^{13} ?
The integral of (2x-4)^{13} is