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

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

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

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

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

Solution steps

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

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

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

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

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

Add a constant to the solution

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

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