What is the integral of 10x-xe^x+e ?

The integral of 10x-xe^x+e is 5x^2-e^xx+e^x+ex+C

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integral of 10x-xe^x+e

\int 10 x - x e^{x} + e d x

5 x^{2} - e^{x} x + e^{x} + e x + C

Solution steps

\int 10 x - x e^{x} + e 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 10 x d x - \int x e^{x} d x + \int e d x

\int 10 x d x = 5 x^{2}

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

\int e d x = e x

= 5 x^{2} - (e^{x} x - e^{x}) + e x

Simplify

= 5 x^{2} - e^{x} x + e^{x} + e x

Add a constant to the solution

= 5 x^{2} - e^{x} x + e^{x} + e x + C

\frac{( 2 x ^{2} + 4 )}{2 x - 2}

\int b x^{3} d x

\frac{x}{1 + x}

\frac{s}{2 s ^{2} + 1}

\frac{d}{d x} (\frac{1}{3} sec^{3} (2 x) - sec (2 x))

What is the integral of 10x-xe^x+e ?
The integral of 10x-xe^x+e is 5x^2-e^xx+e^x+ex+C