What is the integral from 0 to 5 of (8e^{0.2x}+2x) ?

The integral from 0 to 5 of (8e^{0.2x}+2x) is 40e-15

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integral from 0 to 5 of (8e^{0.2x}+2x)

\int_{0}^{5} (8 e^{0.2 x} + 2 x) d x

40 e - 15

Decimal

93.73127 \dots

Solution steps

\int_{0}^{5} 8 e^{0.2 x} + 2 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}^{5} 8 e^{0.2 x} d x + \int_{0}^{5} 2 x d x

\int_{0}^{5} 8 e^{0.2 x} d x = 40 (e - 1)

\int_{0}^{5} 2 x d x = 25

= 40 (e - 1) + 25

Simplify

40 (e - 1) + 25 : 40 e - 15

= 40 e - 15

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What is the integral from 0 to 5 of (8e^{0.2x}+2x) ?
The integral from 0 to 5 of (8e^{0.2x}+2x) is 40e-15