Solve ∫ (from 1 to 2) of 9/3^3-21

$$\int _ { 1 } ^ { 2 } \frac { 9 } { 3 ^ { 3 } - 21 }$$

Evaluate

$$\frac{3}{2}=1.5$$

Solution Steps

Calculate 3 to the power of 3 and get 27.

$$\int _{1}^{2}\frac{9}{27-21}\mathrm{d}x$$

Subtract 21 from 27 to get 6.

$$\int _{1}^{2}\frac{9}{6}\mathrm{d}x$$

Reduce the fraction \frac{9}{6} to lowest terms by extracting and canceling out 3.

$$\int _{1}^{2}\frac{3}{2}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int \frac{3}{2}\mathrm{d}x$$

Find the integral of \frac{3}{2} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{3x}{2}$$

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.

$$\frac{3}{2}\times 2-\frac{3}{2}$$

Simplify.

$$\frac{3}{2}$$