What is the integral of (x^{1/2}+3x+2) ?

The integral of (x^{1/2}+3x+2) is 2/3 x^{3/2}+(3x^2)/2+2x+C

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integral of (x^{1/2}+3x+2)

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

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

Solution steps

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

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

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

\int 2 d x = 2 x

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

Add a constant to the solution

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

θ \to 0 lim (θ cos (θ))

\int \frac{( ln ^{2} ( 3 x ) )}{x} d x

f (x) = \frac{x}{1 + x ^{2}}

\int_{0}^{1} (x x^{2} + 1) d x

\frac{d}{d x} (\frac{120}{( 1 - x ) ^{6}})

What is the integral of (x^{1/2}+3x+2) ?
The integral of (x^{1/2}+3x+2) is 2/3 x^{3/2}+(3x^2)/2+2x+C