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

The integral from 1 to 2 of (e^{3x})/(x^2) is -(e^6)/2+3\Ei(3*2)+e^3-3\Ei(3*1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

- \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

Solution steps

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

Apply Integration By Parts

= [- \frac{e ^{3 x}}{x} - \int - \frac{3 e ^{3 x}}{x} d x]_{1}^{2}

\int - \frac{3 e ^{3 x}}{x} d x = - 3 Ei (3 x)

= [- \frac{e ^{3 x}}{x} - (- 3 Ei (3 x))]_{1}^{2}

Simplify

= [- \frac{e ^{3 x}}{x} + 3 Ei (3 x)]_{1}^{2}

Compute the boundaries:

- \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

= - \frac{e ^{6}}{2} + 3 Ei (3 \cdot 2) + e^{3} - 3 Ei (3 \cdot 1)

What is the integral from 1 to 2 of (e^{3x})/(x^2) ?
The integral from 1 to 2 of (e^{3x})/(x^2) is -(e^6)/2+3\Ei(3*2)+e^3-3\Ei(3*1)