What is the integral from 0 to 1 of (e^x+3)/(e^x) ?

The integral from 0 to 1 of (e^x+3)/(e^x) is -3/e+4

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integral from 0 to 1 of (e^x+3)/(e^x)

\int_{0}^{1} \frac{e ^{x} + 3}{e ^{x}} d x

- \frac{3}{e} + 4

Decimal

2.89636 \dots

Solution steps

\int_{0}^{1} \frac{e ^{x} + 3}{e ^{x}} d x

Expand

\frac{e ^{x} + 3}{e ^{x}} : 1 + \frac{3}{e ^{x}}

= \int_{0}^{1} 1 + \frac{3}{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_{0}^{1} 1 d x + \int_{0}^{1} \frac{3}{e ^{x}} d x

\int_{0}^{1} 1 d x = 1

\int_{0}^{1} \frac{3}{e ^{x}} d x = 3 (- \frac{1}{e} + 1)

= 1 + 3 (- \frac{1}{e} + 1)

Simplify

1 + 3 (- \frac{1}{e} + 1) : - \frac{3}{e} + 4

= - \frac{3}{e} + 4

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What is the integral from 0 to 1 of (e^x+3)/(e^x) ?
The integral from 0 to 1 of (e^x+3)/(e^x) is -3/e+4