What is the integral from 1 to 3 of cos(x)+e^x-2x ?

The integral from 1 to 3 of cos(x)+e^x-2x is sin(3)-sin(1)+e^3-e-8

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integral from 1 to 3 of cos(x)+e^x-2x

\int_{1}^{3} cos (x) + e^{x} - 2 x d x

sin (3) - sin (1) + e^{3} - e - 8

Decimal

8.66690 \dots

Solution steps

\int_{1}^{3} cos (x) + e^{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_{1}^{3} cos (x) d x + \int_{1}^{3} e^{x} d x - \int_{1}^{3} 2 x d x

\int_{1}^{3} cos (x) d x = sin (3) - sin (1)

\int_{1}^{3} e^{x} d x = e^{3} - e

\int_{1}^{3} 2 x d x = 8

= sin (3) - sin (1) + e^{3} - e - 8

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What is the integral from 1 to 3 of cos(x)+e^x-2x ?
The integral from 1 to 3 of cos(x)+e^x-2x is sin(3)-sin(1)+e^3-e-8