Solve ∫ -2^3(3)-2(3)5/2-(3)2

$$\int - 2 ^ { 3 } ( 3 ) - \frac { 2 ( 3 ) 5 } { 2 } - ( 3 ) 2$$

Evaluate

$$С-45x$$

Solution Steps

Calculate 2 to the power of 3 and get 8.

$$\int -8\times 3-\frac{2\times 3\times 5}{2}-3\times 2\mathrm{d}x$$

Multiply -8 and 3 to get -24.

$$\int -24-\frac{2\times 3\times 5}{2}-3\times 2\mathrm{d}x$$

Cancel out 2 and 2.

$$\int -24-3\times 5-3\times 2\mathrm{d}x$$

Multiply 3 and 5 to get 15.

$$\int -24-15-3\times 2\mathrm{d}x$$

Subtract 15 from -24 to get -39.

$$\int -39-3\times 2\mathrm{d}x$$

Multiply 3 and 2 to get 6.

$$\int -39-6\mathrm{d}x$$

Subtract 6 from -39 to get -45.

$$\int -45\mathrm{d}x$$

Find the integral of -45 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$-45x$$

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.

$$-45x+С$$

Differentiate w.r.t. x

$$-45$$