What is the integral from 0 to 0.5 of 2x+3-xe^{3x} ?

The integral from 0 to 0.5 of 2x+3-xe^{3x} is 1.38990…

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integral from 0 to 0.5 of 2x+3-xe^{3x}

\int_{0}^{0.5} 2 x + 3 - x e^{3 x} d x

1.38990 \dots

Solution steps

\int_{0}^{0.5} 2 x + 3 - x e^{3 x} 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_{0}^{0.5} 2 x d x + \int_{0}^{0.5} 3 d x - \int_{0}^{0.5} x e^{3 x} d x

\int_{0}^{0.5} 2 x d x = 0.25

\int_{0}^{0.5} 3 d x = 1.5

\int_{0}^{0.5} x e^{3 x} d x = 0.36009 \dots

= 0.25 + 1.5 - 0.36009 \dots

Simplify

= 1.38990 \dots

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What is the integral from 0 to 0.5 of 2x+3-xe^{3x} ?
The integral from 0 to 0.5 of 2x+3-xe^{3x} is 1.38990…