What is the integral of (x+4)^9 ?

The integral of (x+4)^9 is x(x+4)^9-9/10 (x+4)^{10}+4(x+4)^9+C

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integral of (x+4)^9

\int (x + 4)^{9} d x

x (x + 4)^{9} - \frac{9}{10} (x + 4)^{10} + 4 (x + 4)^{9} + C

Solution steps

\int (x + 4)^{9} d x

Apply Integration By Parts

: (x + 4)^{9} x - \int 9 (x + 4)^{8} x d x

= (x + 4)^{9} x - \int 9 (x + 4)^{8} x d x

\int 9 (x + 4)^{8} x d x = \frac{9}{10} (x + 4)^{10} - 4 (x + 4)^{9}

= (x + 4)^{9} x - (\frac{9}{10} (x + 4)^{10} - 4 (x + 4)^{9})

Simplify

(x + 4)^{9} x - (\frac{9}{10} (x + 4)^{10} - 4 (x + 4)^{9}) : x (x + 4)^{9} - \frac{9}{10} (x + 4)^{10} + 4 (x + 4)^{9}

= x (x + 4)^{9} - \frac{9}{10} (x + 4)^{10} + 4 (x + 4)^{9}

Add a constant to the solution

= x (x + 4)^{9} - \frac{9}{10} (x + 4)^{10} + 4 (x + 4)^{9} + C

f (t) = e^{t} \cdot sin (t)

\frac{d y}{d x} = 4 y (8 - y)

\int \frac{1}{( 4 x - 5 ) ^{2}} d x

n = 1 \sum \infty (1 + \frac{5}{n})^{n}

f (x) = 3 x sin^{2} (x)

What is the integral of (x+4)^9 ?
The integral of (x+4)^9 is x(x+4)^9-9/10 (x+4)^{10}+4(x+4)^9+C