What is the integral from 3 to 7 of (ln(x)+e^x) ?

The integral from 3 to 7 of (ln(x)+e^x) is 7ln(7)-4-3ln(3)+e^7-e^3

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integral from 3 to 7 of (ln(x)+e^x)

\int_{3}^{7} (ln (x) + e^{x}) d x

7 ln (7) - 4 - 3 ln (3) + e^{7} - e^{3}

Decimal Notation

1082.87315 \dots

Solution steps

\int_{3}^{7} ln (x) + e^{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_{3}^{7} ln (x) d x + \int_{3}^{7} e^{x} d x

\int_{3}^{7} ln (x) d x = 7 ln (7) - 4 - 3 ln (3)

\int_{3}^{7} e^{x} d x = e^{7} - e^{3}

= 7 ln (7) - 4 - 3 ln (3) + e^{7} - e^{3}

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What is the integral from 3 to 7 of (ln(x)+e^x) ?
The integral from 3 to 7 of (ln(x)+e^x) is 7ln(7)-4-3ln(3)+e^7-e^3