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Popular >

integral of (3-2x)^{11}

Solution

\int (3 - 2 x)^{11} d x

Solution

177147 x - 649539 x^{2} + 1443420 x^{3} - 2165130 x^{4} + 2309472 x^{5} - 1796256 x^{6} + 1026432 x^{7} - 427680 x^{8} + 126720 x^{9} - 25344 x^{10} + 3072 x^{11} - \frac{512 x ^{12}}{3} + C

Solution steps

\int (3 - 2 x)^{11} d x

Expand

(3 - 2 x)^{11} : 177147 - 1299078 x + 4330260 x^{2} - 8660520 x^{3} + 11547360 x^{4} - 10777536 x^{5} + 7185024 x^{6} - 3421440 x^{7} + 1140480 x^{8} - 253440 x^{9} + 33792 x^{10} - 2048 x^{11}

= \int 177147 - 1299078 x + 4330260 x^{2} - 8660520 x^{3} + 11547360 x^{4} - 10777536 x^{5} + 7185024 x^{6} - 3421440 x^{7} + 1140480 x^{8} - 253440 x^{9} + 33792 x^{10} - 2048 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 177147 d x - \int 1299078 x d x + \int 4330260 x^{2} d x - \int 8660520 x^{3} d x + \int 11547360 x^{4} d x - \int 10777536 x^{5} d x + \int 7185024 x^{6} d x - \int 3421440 x^{7} d x + \int 1140480 x^{8} d x - \int 253440 x^{9} d x + \int 33792 x^{10} d x - \int 2048 x^{11} d x

\int 177147 d x = 177147 x

\int 1299078 x d x = 649539 x^{2}

\int 4330260 x^{2} d x = 1443420 x^{3}

\int 8660520 x^{3} d x = 2165130 x^{4}

\int 11547360 x^{4} d x = 2309472 x^{5}

\int 10777536 x^{5} d x = 1796256 x^{6}

\int 7185024 x^{6} d x = 1026432 x^{7}

\int 3421440 x^{7} d x = 427680 x^{8}

\int 1140480 x^{8} d x = 126720 x^{9}

\int 253440 x^{9} d x = 25344 x^{10}

\int 33792 x^{10} d x = 3072 x^{11}

\int 2048 x^{11} d x = \frac{512 x ^{12}}{3}

= 177147 x - 649539 x^{2} + 1443420 x^{3} - 2165130 x^{4} + 2309472 x^{5} - 1796256 x^{6} + 1026432 x^{7} - 427680 x^{8} + 126720 x^{9} - 25344 x^{10} + 3072 x^{11} - \frac{512 x ^{12}}{3}

Add a constant to the solution

= 177147 x - 649539 x^{2} + 1443420 x^{3} - 2165130 x^{4} + 2309472 x^{5} - 1796256 x^{6} + 1026432 x^{7} - 427680 x^{8} + 126720 x^{9} - 25344 x^{10} + 3072 x^{11} - \frac{512 x ^{12}}{3} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (3-2x)^{11} ?
The integral of (3-2x)^{11} is