What is the integral from 2 to 6 of (2x+1)e^{0.4x} ?

The integral from 2 to 6 of (2x+1)e^{0.4x} is 220.46352…

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integral from 2 to 6 of (2x+1)e^{0.4x}

\int_{2}^{6} (2 x + 1) e^{0.4 x} d x

220.46352 \dots

Solution steps

\int_{2}^{6} (2 x + 1) e^{0.4 x} d x

Expand

(2 x + 1) e^{0.4 x} : 2 e^{0.4 x} x + e^{0.4 x}

= \int_{2}^{6} 2 e^{0.4 x} x + e^{0.4 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_{2}^{6} 2 e^{0.4 x} x d x + \int_{2}^{6} e^{0.4 x} d x

\int_{2}^{6} 2 e^{0.4 x} x d x = 198.46943 \dots

\int_{2}^{6} e^{0.4 x} d x = 21.99408 \dots

= 198.46943 \dots + 21.99408 \dots

Simplify

= 220.46352 \dots

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What is the integral from 2 to 6 of (2x+1)e^{0.4x} ?
The integral from 2 to 6 of (2x+1)e^{0.4x} is 220.46352…