What is the integral from 3 to 7 of (2x+1)e^{0.4x} ?

The integral from 3 to 7 of (2x+1)e^{0.4x} is 394.51558…

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integral from 3 to 7 of (2x+1)e^{0.4x}

\int_{3}^{7} (2 x + 1) e^{0.4 x} d x

394.51558 \dots

Solution steps

\int_{3}^{7} (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_{3}^{7} 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_{3}^{7} 2 e^{0.4 x} x d x + \int_{3}^{7} e^{0.4 x} d x

\int_{3}^{7} 2 e^{0.4 x} x d x = 361.70426 \dots

\int_{3}^{7} e^{0.4 x} d x = 32.81132 \dots

= 361.70426 \dots + 32.81132 \dots

Simplify

= 394.51558 \dots

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What is the integral from 3 to 7 of (2x+1)e^{0.4x} ?
The integral from 3 to 7 of (2x+1)e^{0.4x} is 394.51558…