What is the integral of 4x+sqrt(x) ?

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

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integral of 4x+sqrt(x)

\int 4 x + x d x

2 x^{2} + \frac{2}{3} x^{\frac{3}{2}} + C

Solution steps

\int 4 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 d x

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

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

= 2 x^{2} + \frac{2}{3} x^{\frac{3}{2}}

Add a constant to the solution

= 2 x^{2} + \frac{2}{3} x^{\frac{3}{2}} + C

5 x^{3} + 10 x^{2} - 2 x + 1

x^{2} - 2 x + 1

2 x y + 6 x + (x^{2} - 4) y^{^{'}} = 0

y = (9 x + 5) x^{2}

n = 1 \sum \infty \frac{1 ^{n}}{n + 2}

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