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Popular >

integral of (x+4)^{14}

Solution

\int (x + 4)^{14} d x

Solution

\frac{x ^{15}}{15} + 4 x^{14} + 112 x^{13} + \frac{5824 x ^{12}}{3} + 23296 x^{11} + \frac{1025024 x ^{10}}{5} + \frac{4100096 x ^{9}}{3} + 7028736 x^{8} + 28114944 x^{7} + \frac{262406144 x ^{6}}{3} + \frac{1049624576 x ^{5}}{5} + 381681664 x^{4} + \frac{1526726656 x ^{3}}{3} + 469762048 x^{2} + 268435456 x + C

Solution steps

\int (x + 4)^{14} d x

Expand

(x + 4)^{14} : x^{14} + 56 x^{13} + 1456 x^{12} + 23296 x^{11} + 256256 x^{10} + 2050048 x^{9} + 12300288 x^{8} + 56229888 x^{7} + 196804608 x^{6} + 524812288 x^{5} + 1049624576 x^{4} + 1526726656 x^{3} + 1526726656 x^{2} + 939524096 x + 268435456

= \int x^{14} + 56 x^{13} + 1456 x^{12} + 23296 x^{11} + 256256 x^{10} + 2050048 x^{9} + 12300288 x^{8} + 56229888 x^{7} + 196804608 x^{6} + 524812288 x^{5} + 1049624576 x^{4} + 1526726656 x^{3} + 1526726656 x^{2} + 939524096 x + 268435456 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^{14} d x + \int 56 x^{13} d x + \int 1456 x^{12} d x + \int 23296 x^{11} d x + \int 256256 x^{10} d x + \int 2050048 x^{9} d x + \int 12300288 x^{8} d x + \int 56229888 x^{7} d x + \int 196804608 x^{6} d x + \int 524812288 x^{5} d x + \int 1049624576 x^{4} d x + \int 1526726656 x^{3} d x + \int 1526726656 x^{2} d x + \int 939524096 x d x + \int 268435456 d x

\int x^{14} d x = \frac{x ^{15}}{15}

\int 56 x^{13} d x = 4 x^{14}

\int 1456 x^{12} d x = 112 x^{13}

\int 23296 x^{11} d x = \frac{5824 x ^{12}}{3}

\int 256256 x^{10} d x = 23296 x^{11}

\int 2050048 x^{9} d x = \frac{1025024 x ^{10}}{5}

\int 12300288 x^{8} d x = \frac{4100096 x ^{9}}{3}

\int 56229888 x^{7} d x = 7028736 x^{8}

\int 196804608 x^{6} d x = 28114944 x^{7}

\int 524812288 x^{5} d x = \frac{262406144 x ^{6}}{3}

\int 1049624576 x^{4} d x = \frac{1049624576 x ^{5}}{5}

\int 1526726656 x^{3} d x = 381681664 x^{4}

\int 1526726656 x^{2} d x = \frac{1526726656 x ^{3}}{3}

\int 939524096 x d x = 469762048 x^{2}

\int 268435456 d x = 268435456 x

= \frac{x ^{15}}{15} + 4 x^{14} + 112 x^{13} + \frac{5824 x ^{12}}{3} + 23296 x^{11} + \frac{1025024 x ^{10}}{5} + \frac{4100096 x ^{9}}{3} + 7028736 x^{8} + 28114944 x^{7} + \frac{262406144 x ^{6}}{3} + \frac{1049624576 x ^{5}}{5} + 381681664 x^{4} + \frac{1526726656 x ^{3}}{3} + 469762048 x^{2} + 268435456 x

Add a constant to the solution

= \frac{x ^{15}}{15} + 4 x^{14} + 112 x^{13} + \frac{5824 x ^{12}}{3} + 23296 x^{11} + \frac{1025024 x ^{10}}{5} + \frac{4100096 x ^{9}}{3} + 7028736 x^{8} + 28114944 x^{7} + \frac{262406144 x ^{6}}{3} + \frac{1049624576 x ^{5}}{5} + 381681664 x^{4} + \frac{1526726656 x ^{3}}{3} + 469762048 x^{2} + 268435456 x + C

Graph

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Frequently Asked Questions (FAQ)

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