What is the integral of (x(3x-sqrt(x))+(e^{ex}+8)) ?

The integral of (x(3x-sqrt(x))+(e^{ex}+8)) is x^3-2/5 x^{5/2}+e^{ex-1}+8x+C

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integral of (x(3x-sqrt(x))+(e^{ex}+8))

\int (x (3 x - x) + (e^{e x} + 8)) d x

x^{3} - \frac{2}{5} x^{\frac{5}{2}} + e^{e x - 1} + 8 x + C

Solution steps

\int x (3 x - x) + e^{e x} + 8 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 (3 x - x) d x + \int e^{e x} d x + \int 8 d x

\int x (3 x - x) d x = x^{3} - \frac{2}{5} x^{\frac{5}{2}}

\int e^{e x} d x = e^{e x - 1}

\int 8 d x = 8 x

= x^{3} - \frac{2}{5} x^{\frac{5}{2}} + e^{e x - 1} + 8 x

Add a constant to the solution

= x^{3} - \frac{2}{5} x^{\frac{5}{2}} + e^{e x - 1} + 8 x + C

What is the integral of (x(3x-sqrt(x))+(e^{ex}+8)) ?
The integral of (x(3x-sqrt(x))+(e^{ex}+8)) is x^3-2/5 x^{5/2}+e^{ex-1}+8x+C