What is the integral of 4sqrt(x)-xsqrt(x) ?

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

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integral of 4sqrt(x)-xsqrt(x)

\int 4 x - x x d x

\frac{8}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

Solution steps

\int 4 x - x x 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 4 x d x - \int x x d x

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

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

= \frac{8}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}}

Add a constant to the solution

= \frac{8}{3} x^{\frac{3}{2}} - \frac{2}{5} x^{\frac{5}{2}} + C

\frac{d}{d x} (\frac{9}{4 - x})

f (x) = 3 x^{3}, at x = 3

\frac{\partial}{\partial x} (x^{2} e^{y} + x - 2 y)

\int \frac{x ^{2} + 2 x + 1}{x ^{3} + x} d x

\frac{d y}{d x} = e^{y - x^{2} + 1}

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