Solve ∫ (from - 6 to 13) of 2+1(-10)-3/2(-3)-(-5)/-6-(-5)+(-10)

$$\int _ { - 6 } ^ { 13 } \frac { 2 + \frac { 1 ( - 10 ) - 3 } { 2 ( - 3 ) - ( - 5 ) } } { - 6 - ( - 5 ) + ( - 10 ) }$$

Evaluate

$$-\frac{285}{11}\approx -25.909090909$$

Solution Steps

Multiply 1 and -10 to get -10.

$$\int _{-6}^{13}\frac{2+\frac{-10-3}{2\left(-3\right)-\left(-5\right)}}{-6-\left(-5\right)-10}\mathrm{d}x$$

Subtract 3 from -10 to get -13.

$$\int _{-6}^{13}\frac{2+\frac{-13}{2\left(-3\right)-\left(-5\right)}}{-6-\left(-5\right)-10}\mathrm{d}x$$

Multiply 2 and -3 to get -6.

$$\int _{-6}^{13}\frac{2+\frac{-13}{-6-\left(-5\right)}}{-6-\left(-5\right)-10}\mathrm{d}x$$

The opposite of -5 is 5.

$$\int _{-6}^{13}\frac{2+\frac{-13}{-6+5}}{-6-\left(-5\right)-10}\mathrm{d}x$$

Add -6 and 5 to get -1.

$$\int _{-6}^{13}\frac{2+\frac{-13}{-1}}{-6-\left(-5\right)-10}\mathrm{d}x$$

Fraction \frac{-13}{-1} can be simplified to 13 by removing the negative sign from both the numerator and the denominator.

$$\int _{-6}^{13}\frac{2+13}{-6-\left(-5\right)-10}\mathrm{d}x$$

Add 2 and 13 to get 15.

$$\int _{-6}^{13}\frac{15}{-6-\left(-5\right)-10}\mathrm{d}x$$

The opposite of -5 is 5.

$$\int _{-6}^{13}\frac{15}{-6+5-10}\mathrm{d}x$$

Add -6 and 5 to get -1.

$$\int _{-6}^{13}\frac{15}{-1-10}\mathrm{d}x$$

Subtract 10 from -1 to get -11.

$$\int _{-6}^{13}\frac{15}{-11}\mathrm{d}x$$

Fraction \frac{15}{-11} can be rewritten as -\frac{15}{11} by extracting the negative sign.

$$\int _{-6}^{13}-\frac{15}{11}\mathrm{d}x$$

Evaluate the indefinite integral first.

$$\int -\frac{15}{11}\mathrm{d}x$$

Find the integral of -\frac{15}{11} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-\frac{15x}{11}$$

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.

$$-\frac{15}{11}\times 13+\frac{15}{11}\left(-6\right)$$

Simplify.

$$-\frac{285}{11}$$