What is the integral of 10e^t-te^t+1 ?

The integral of 10e^t-te^t+1 is -e^tt+t+11e^t+C

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integral of 10e^t-te^t+1

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

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

Solution steps

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

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^{t} d t - \int t e^{t} d t + \int 1 d t

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

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

\int 1 d t = t

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

Simplify

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

Add a constant to the solution

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

What is the integral of 10e^t-te^t+1 ?
The integral of 10e^t-te^t+1 is -e^tt+t+11e^t+C