What is the integral of (x+5)^9 ?

The integral of (x+5)^9 is x(x+5)^9-9/10 (x+5)^{10}+5(x+5)^9+C

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integral of (x+5)^9

\int (x + 5)^{9} d x

x (x + 5)^{9} - \frac{9}{10} (x + 5)^{10} + 5 (x + 5)^{9} + C

Solution steps

\int (x + 5)^{9} d x

Apply Integration By Parts

: (x + 5)^{9} x - \int 9 (x + 5)^{8} x d x

= (x + 5)^{9} x - \int 9 (x + 5)^{8} x d x

\int 9 (x + 5)^{8} x d x = \frac{9}{10} (x + 5)^{10} - 5 (x + 5)^{9}

= (x + 5)^{9} x - (\frac{9}{10} (x + 5)^{10} - 5 (x + 5)^{9})

Simplify

(x + 5)^{9} x - (\frac{9}{10} (x + 5)^{10} - 5 (x + 5)^{9}) : x (x + 5)^{9} - \frac{9}{10} (x + 5)^{10} + 5 (x + 5)^{9}

= x (x + 5)^{9} - \frac{9}{10} (x + 5)^{10} + 5 (x + 5)^{9}

Add a constant to the solution

= x (x + 5)^{9} - \frac{9}{10} (x + 5)^{10} + 5 (x + 5)^{9} + C

\int x^{2} 5 x + 4 d x

f (x) = x^{3} - 6 x^{2} + 8, g (x) = x^{2} - 4 x

\frac{d y}{d x} = (x - 8) e^{- 2 y}

f (x) = 2 x + 6

2 x^{2} + x y + y^{2} = 4

What is the integral of (x+5)^9 ?
The integral of (x+5)^9 is x(x+5)^9-9/10 (x+5)^{10}+5(x+5)^9+C