What is the integral from 1 to 7 of (5/x-e^{2-3x}) ?

The integral from 1 to 7 of (5/x-e^{2-3x}) is 5ln(7)-(1/e-1/(e^{19)})/3

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integral from 1 to 7 of (5/x-e^{2-3x})

\int_{1}^{7} (\frac{5}{x} - e^{2 - 3 x}) d x

5 ln (7) - \frac{\frac{1}{e} - \frac{1}{e ^{19}}}{3}

Decimal

9.60692 \dots

Solution steps

\int_{1}^{7} \frac{5}{x} - e^{2 - 3 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}^{7} \frac{5}{x} d x - \int_{1}^{7} e^{2 - 3 x} d x

\int_{1}^{7} \frac{5}{x} d x = 5 ln (7)

\int_{1}^{7} e^{2 - 3 x} d x = \frac{\frac{1}{e} - \frac{1}{e ^{19}}}{3}

= 5 ln (7) - \frac{\frac{1}{e} - \frac{1}{e ^{19}}}{3}

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What is the integral from 1 to 7 of (5/x-e^{2-3x}) ?
The integral from 1 to 7 of (5/x-e^{2-3x}) is 5ln(7)-(1/e-1/(e^{19)})/3