What is the integral from 1 to 3 of 2pix((e^x)/x) ?

The integral from 1 to 3 of 2pix((e^x)/x) is 2pi(e^3-e)

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integral from 1 to 3 of 2pix((e^x)/x)

\int_{1}^{3} 2 π x (\frac{e ^{x}}{x}) d x

2 π (e^{3} - e)

Decimal

109.12168 \dots

Solution steps

\int_{1}^{3} 2 π x \frac{e ^{x}}{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 π \cdot \int_{1}^{3} x \frac{e ^{x}}{x} d x

Simplify

x \frac{e ^{x}}{x} : e^{x}

= 2 π \cdot \int_{1}^{3} e^{x} d x

Use the common integral:

\int e^{x} d x = e^{x}

= 2 π [e^{x}]_{1}^{3}

Compute the boundaries:

e^{3} - e

= 2 π (e^{3} - e)

\int \frac{1}{X} d X

\int \frac{2 x}{e ^{x^{2}}} d x

\int_{6}^{8} \frac{18}{( x - 6 ) ^{3}} d x

\int_{6}^{7} π (2 x + 2)^{2} d x

\frac{d y}{d x}, x^{2} + y = 1

What is the integral from 1 to 3 of 2pix((e^x)/x) ?
The integral from 1 to 3 of 2pix((e^x)/x) is 2pi(e^3-e)