What is the integral of (x^{3/2}+8x+9) ?

The integral of (x^{3/2}+8x+9) is 2/5 x^{5/2}+4x^2+9x+C

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integral of (x^{3/2}+8x+9)

\int (x^{\frac{3}{2}} + 8 x + 9) d x

\frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 9 x + C

Solution steps

\int x^{\frac{3}{2}} + 8 x + 9 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^{\frac{3}{2}} d x + \int 8 x d x + \int 9 d x

\int x^{\frac{3}{2}} d x = \frac{2}{5} x^{\frac{5}{2}}

\int 8 x d x = 4 x^{2}

\int 9 d x = 9 x

= \frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 9 x

Add a constant to the solution

= \frac{2}{5} x^{\frac{5}{2}} + 4 x^{2} + 9 x + C

f (x) = - 3 x^{2} + 6 x + 4, at x = 1

x \to 0 lim (\frac{ln ( x + 2 )}{x})

\frac{d y}{d x} = \frac{y}{y - x}

y = x^{2}, y = 9

x^{\frac{7}{2}}

What is the integral of (x^{3/2}+8x+9) ?
The integral of (x^{3/2}+8x+9) is 2/5 x^{5/2}+4x^2+9x+C