What is the integral of (x+3)^9 ?

The integral of (x+3)^9 is (x+3)^9x-9(((x+3)^{10}}{10}-\frac{(x+3)^9)/3)+C

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integral of (x+3)^9

\int (x + 3)^{9} d x

(x + 3)^{9} x - 9 (\frac{( x + 3 ) ^{10}}{10} - \frac{( x + 3 ) ^{9}}{3}) + C

Solution steps

\int (x + 3)^{9} d x

Apply Integration By Parts

: (x + 3)^{9} x - \int 9 (x + 3)^{8} x d x

= (x + 3)^{9} x - \int 9 (x + 3)^{8} x d x

\int 9 (x + 3)^{8} x d x = 9 (\frac{( x + 3 ) ^{10}}{10} - \frac{( x + 3 ) ^{9}}{3})

= (x + 3)^{9} x - 9 (\frac{( x + 3 ) ^{10}}{10} - \frac{( x + 3 ) ^{9}}{3})

Add a constant to the solution

= (x + 3)^{9} x - 9 (\frac{( x + 3 ) ^{10}}{10} - \frac{( x + 3 ) ^{9}}{3}) + C

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What is the integral of (x+3)^9 ?
The integral of (x+3)^9 is (x+3)^9x-9(((x+3)^{10}}{10}-\frac{(x+3)^9)/3)+C