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

y = x, at x = \frac{1}{4}

\int \frac{ln ^{5} ( x ^{2} )}{x} d x

\frac{d}{d x} (- 6 x^{2} + 6 x)

\int 2 (3 - e^{- t}) d t

\frac{2}{s ^{2} + 4 s + 3}

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