What is the integral from 0 to 1 of e^t+4te^t ?

The integral from 0 to 1 of e^t+4te^t is e+3

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integral from 0 to 1 of e^t+4te^t

\int_{0}^{1} e^{t} + 4 t e^{t} d t

e + 3

Decimal Notation

5.71828 \dots

Solution steps

\int_{0}^{1} e^{t} + 4 t e^{t} 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_{0}^{1} e^{t} d t + \int_{0}^{1} 4 t e^{t} d t

\int_{0}^{1} e^{t} d t = e - 1

\int_{0}^{1} 4 t e^{t} d t = 4

= e - 1 + 4

Simplify

= e + 3

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What is the integral from 0 to 1 of e^t+4te^t ?
The integral from 0 to 1 of e^t+4te^t is e+3