What is the integral of 2sqrt(x)+3 ?

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

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integral of 2sqrt(x)+3

\int 2 x + 3 d x

\frac{4}{3} x^{\frac{3}{2}} + 3 x + C

Solution steps

\int 2 x + 3 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 2 x d x + \int 3 d x

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

\int 3 d x = 3 x

= \frac{4}{3} x^{\frac{3}{2}} + 3 x

Add a constant to the solution

= \frac{4}{3} x^{\frac{3}{2}} + 3 x + C

x \to 0 lim (x^{x^{x}} - 1)

d er i v a t i v e \frac{x ^{2}}{3} + \frac{1}{x ^{2}}

y y^{^{'}} = - 2 x (1 + y^{2})

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

t an g e n t f (x) = x^{3}, a

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