Solve ∫ (from 2 to 3) of log_{2}3

$$\int _ { 2 } ^ { 3 } \log _ { 2 } 3$$

Evaluate

$$\log_{2}\left(3\right)\approx 1.584962501$$

Solution Steps

Evaluate the indefinite integral first.

$$\int \log_{2}\left(3\right)\mathrm{d}x$$

Find the integral of \log_{2}\left(3\right) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\log_{2}\left(3\right)x$$

Simplify.

$$x\log_{2}\left(3\right)$$

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.

$$\ln(3)\ln(2)^{-1}\times 3-\ln(3)\ln(2)^{-1}\times 2$$

Simplify.

$$\log_{2}\left(3\right)$$