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Popular >

integral of (x+3)^{11}

Solution

\int (x + 3)^{11} d x

Solution

x (x + 3)^{11} - \frac{11 x ^{12}}{12} - 30 x^{11} - \frac{891 x ^{10}}{2} - 3960 x^{9} - \frac{93555 x ^{8}}{4} - 96228 x^{7} - 280665 x^{6} - 577368 x^{5} - \frac{3247695 x ^{4}}{4} - 721710 x^{3} - \frac{649539 x ^{2}}{2} + C

Solution steps

\int (x + 3)^{11} d x

Apply Integration By Parts

: (x + 3)^{11} x - \int 11 (x + 3)^{10} x d x

= (x + 3)^{11} x - \int 11 (x + 3)^{10} x d x

\int 11 (x + 3)^{10} x d x = \frac{11 x ^{12}}{12} + 30 x^{11} + \frac{891 x ^{10}}{2} + 3960 x^{9} + \frac{93555 x ^{8}}{4} + 96228 x^{7} + 280665 x^{6} + 577368 x^{5} + \frac{3247695 x ^{4}}{4} + 721710 x^{3} + \frac{649539 x ^{2}}{2}

= (x + 3)^{11} x - (\frac{11 x ^{12}}{12} + 30 x^{11} + \frac{891 x ^{10}}{2} + 3960 x^{9} + \frac{93555 x ^{8}}{4} + 96228 x^{7} + 280665 x^{6} + 577368 x^{5} + \frac{3247695 x ^{4}}{4} + 721710 x^{3} + \frac{649539 x ^{2}}{2})

Simplify

(x + 3)^{11} x - (\frac{11 x ^{12}}{12} + 30 x^{11} + \frac{891 x ^{10}}{2} + 3960 x^{9} + \frac{93555 x ^{8}}{4} + 96228 x^{7} + 280665 x^{6} + 577368 x^{5} + \frac{3247695 x ^{4}}{4} + 721710 x^{3} + \frac{649539 x ^{2}}{2}) : x (x + 3)^{11} - \frac{11 x ^{12}}{12} - 30 x^{11} - \frac{891 x ^{10}}{2} - 3960 x^{9} - \frac{93555 x ^{8}}{4} - 96228 x^{7} - 280665 x^{6} - 577368 x^{5} - \frac{3247695 x ^{4}}{4} - 721710 x^{3} - \frac{649539 x ^{2}}{2}

= x (x + 3)^{11} - \frac{11 x ^{12}}{12} - 30 x^{11} - \frac{891 x ^{10}}{2} - 3960 x^{9} - \frac{93555 x ^{8}}{4} - 96228 x^{7} - 280665 x^{6} - 577368 x^{5} - \frac{3247695 x ^{4}}{4} - 721710 x^{3} - \frac{649539 x ^{2}}{2}

Add a constant to the solution

= x (x + 3)^{11} - \frac{11 x ^{12}}{12} - 30 x^{11} - \frac{891 x ^{10}}{2} - 3960 x^{9} - \frac{93555 x ^{8}}{4} - 96228 x^{7} - 280665 x^{6} - 577368 x^{5} - \frac{3247695 x ^{4}}{4} - 721710 x^{3} - \frac{649539 x ^{2}}{2} + C

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Frequently Asked Questions (FAQ)

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