Solve ∫ (from 4 to 6) of x/xln(1.5) wrt x

$$\int _ { 4 } ^ { 6 } \frac { x } { x \ln ( 1.5 ) } d x$$

Evaluate

$$\frac{2}{\ln(1.5)}\approx 4.932606925$$

Solution Steps

Cancel out x in both numerator and denominator.

$$\int _{4}^{6}\frac{1}{\log_{e}\left(1.5\right)}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{1}{\log_{e}\left(1.5\right)}\mathrm{d}x$$

Find the integral of \frac{1}{\log_{e}\left(1.5\right)} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x}{\log_{e}\left(1.5\right)}$$

Simplify.

$$\frac{x}{\ln(\frac{3}{2})}$$

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.

$$\left(\ln(3)-\ln(2)\right)^{-1}\times 6-\left(\ln(3)-\ln(2)\right)^{-1}\times 4$$

Simplify.

$$\frac{2}{\ln(\frac{3}{2})}$$