What is the integral from 2 to 5 of cos(x)+e^x-2x ?

The integral from 2 to 5 of cos(x)+e^x-2x is sin(5)-sin(2)+e^5-e^2-21

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integral from 2 to 5 of cos(x)+e^x-2x

\int_{2}^{5} cos (x) + e^{x} - 2 x d x

sin (5) - sin (2) + e^{5} - e^{2} - 21

Decimal

118.15588 \dots

Solution steps

\int_{2}^{5} 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_{2}^{5} cos (x) d x + \int_{2}^{5} e^{x} d x - \int_{2}^{5} 2 x d x

\int_{2}^{5} cos (x) d x = sin (5) - sin (2)

\int_{2}^{5} e^{x} d x = e^{5} - e^{2}

\int_{2}^{5} 2 x d x = 21

= sin (5) - sin (2) + e^{5} - e^{2} - 21

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

\int_{6}^{\infty} \frac{2}{x ^{3}} d x

What is the integral from 2 to 5 of cos(x)+e^x-2x ?
The integral from 2 to 5 of cos(x)+e^x-2x is sin(5)-sin(2)+e^5-e^2-21