What is the integral from-3 to-2 of (2e^{-0.1y}+3/y) ?

The integral from-3 to-2 of (2e^{-0.1y}+3/y) is 1.35272…

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integral from-3 to-2 of (2e^{-0.1y}+3/y)

\int_{- 3}^{- 2} (2 e^{- 0.1 y} + \frac{3}{y}) d y

1.35272 \dots

Solution steps

\int_{- 3}^{- 2} 2 e^{- 0.1 y} + \frac{3}{y} d y

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}^{- 2} 2 e^{- 0.1 y} d y + \int_{- 3}^{- 2} \frac{3}{y} d y

\int_{- 3}^{- 2} 2 e^{- 0.1 y} d y = 2.56912 \dots

\int_{- 3}^{- 2} \frac{3}{y} d y = 3 (ln (2) - ln (3))

= 2.56912 \dots + 3 (ln (2) - ln (3))

Simplify

2.56912 \dots + 3 (ln (2) - ln (3)) : 1.35272 \dots

= 1.35272 \dots

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What is the integral from-3 to-2 of (2e^{-0.1y}+3/y) ?
The integral from-3 to-2 of (2e^{-0.1y}+3/y) is 1.35272…