Solve ∫ (from 1 to 2) of 2x1/x wrt x

$$\int _ { 1 } ^ { 2 } 2 x \frac { 1 } { x } d x$$

Evaluate

$$2$$

Solution Steps

Express 2\times \frac{1}{x} as a single fraction.

$$\int _{1}^{2}\frac{2}{x}x\mathrm{d}x$$

Cancel out x and x.

$$\int _{1}^{2}2\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int 2\mathrm{d}x$$

Find the integral of 2 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$2x$$

The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.

$$2\times 2-2$$

Simplify.

$$2$$