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

The integral from 0 to 1 of ((e^x+4))/(e^x) is -4/e+5

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integral from 0 to 1 of ((e^x+4))/(e^x)

\int_{0}^{1} \frac{( e ^{x} + 4 )}{e ^{x}} d x

- \frac{4}{e} + 5

Decimal

3.52848 \dots

Solution steps

\int_{0}^{1} \frac{e ^{x} + 4}{e ^{x}} d x

Expand

\frac{e ^{x} + 4}{e ^{x}} : 1 + \frac{4}{e ^{x}}

= \int_{0}^{1} 1 + \frac{4}{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{4}{e ^{x}} d x

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

\int_{0}^{1} \frac{4}{e ^{x}} d x = 4 (- \frac{1}{e} + 1)

= 1 + 4 (- \frac{1}{e} + 1)

Simplify

1 + 4 (- \frac{1}{e} + 1) : - \frac{4}{e} + 5

= - \frac{4}{e} + 5

What is the integral from 0 to 1 of ((e^x+4))/(e^x) ?
The integral from 0 to 1 of ((e^x+4))/(e^x) is -4/e+5