Solve ∫ (-7)-3/(5)(3)-6+(-3)-1

$$\int \frac { ( - 7 ) - 3 } { ( 5 ) ( 3 ) - 6 + ( - 3 ) - 1 }$$

Evaluate

$$С-2x$$

Solution Steps

Subtract 3 from -7 to get -10.

$$\int \frac{-10}{5\times 3-6-3-1}\mathrm{d}x$$

Multiply 5 and 3 to get 15.

$$\int \frac{-10}{15-6-3-1}\mathrm{d}x$$

Subtract 6 from 15 to get 9.

$$\int \frac{-10}{9-3-1}\mathrm{d}x$$

Subtract 3 from 9 to get 6.

$$\int \frac{-10}{6-1}\mathrm{d}x$$

Subtract 1 from 6 to get 5.

$$\int \frac{-10}{5}\mathrm{d}x$$

Divide -10 by 5 to get -2.

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

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

$$-2x$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$-2x+С$$

Differentiate w.r.t. x

$$-2$$