What is the integral of (x^{3/2}+4x+4) ?

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

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integral of (x^{3/2}+4x+4)

\int (x^{\frac{3}{2}} + 4 x + 4) d x

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

Solution steps

\int x^{\frac{3}{2}} + 4 x + 4 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 4 x d x + \int 4 d x

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

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

\int 4 d x = 4 x

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

Add a constant to the solution

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

\frac{d}{d x} (- \frac{64}{( 1 + 8 x ) ^{2}})

f (x) = 5 tan (x), at x = \frac{π}{3}

\int \frac{x + 1}{x - 3} d x

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

f (x) = cos^{2} (2 x)

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