What is the integral of 10e^x-xe^x+1 ?

The integral of 10e^x-xe^x+1 is -e^xx+x+11e^x+C

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integral of 10e^x-xe^x+1

\int 10 e^{x} - x e^{x} + 1 d x

- e^{x} x + x + 11 e^{x} + C

Solution steps

\int 10 e^{x} - x e^{x} + 1 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 e^{x} d x - \int x e^{x} d x + \int 1 d x

\int 10 e^{x} d x = 10 e^{x}

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

\int 1 d x = x

= 10 e^{x} - (e^{x} x - e^{x}) + x

Simplify

= - e^{x} x + x + 11 e^{x}

Add a constant to the solution

= - e^{x} x + x + 11 e^{x} + C

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What is the integral of 10e^x-xe^x+1 ?
The integral of 10e^x-xe^x+1 is -e^xx+x+11e^x+C