What is the integral of ((4-x)^2)/(sqrt(x)) ?

The integral of ((4-x)^2)/(sqrt(x)) is 2/5 x^2sqrt(x)-16/3 xsqrt(x)+32sqrt(x)+C

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integral of ((4-x)^2)/(sqrt(x))

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

\frac{2}{5} x^{2} x - \frac{16}{3} x x + 32 x + C

Solution steps

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

Apply Integration By Parts

: x (4 - x)^{2} - \int \frac{3 x ^{2} - 8 x - 16}{2 x} d x

= x (4 - x)^{2} - \int \frac{3 x ^{2} - 8 x - 16}{2 x} d x

\int \frac{3 x ^{2} - 8 x - 16}{2 x} d x = \frac{1}{15} x (9 x^{2} - 40 x - 240)

= x (4 - x)^{2} - \frac{1}{15} x (9 x^{2} - 40 x - 240)

Simplify

x (4 - x)^{2} - \frac{1}{15} x (9 x^{2} - 40 x - 240) : \frac{2}{5} x^{2} x - \frac{16}{3} x x + 32 x

= \frac{2}{5} x^{2} x - \frac{16}{3} x x + 32 x

Add a constant to the solution

= \frac{2}{5} x^{2} x - \frac{16}{3} x x + 32 x + C

\frac{e ^{x}}{e ^{x} + 3}

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

\int \frac{4 x}{x ^{2} + 1} d x

\int x^{2} \cdot 2^{x} d x

f (x) = x + x^{\frac{2}{3}} - 3 x

What is the integral of ((4-x)^2)/(sqrt(x)) ?
The integral of ((4-x)^2)/(sqrt(x)) is 2/5 x^2sqrt(x)-16/3 xsqrt(x)+32sqrt(x)+C