Solve ∫ (3^{2}+3):(-3)-2^2*(-5)(-6+2^3)*(-5)^2-7^0

$$\int ( 3 ^ { 2 } + 3 ) : ( - 3 ) - 2 ^ { 2 } \cdot ( - 5 ) ( - 6 + 2 ^ { 3 } ) \cdot ( - 5 ) ^ { 2 } - 7 ^ { 0 }$$

Evaluate

$$995x+С$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$\int \frac{3^{2}+3}{-3}-2^{2}\left(-5\right)^{3}\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Calculate 3 to the power of 2 and get 9.

$$\int \frac{9+3}{-3}-2^{2}\left(-5\right)^{3}\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Add 9 and 3 to get 12.

$$\int \frac{12}{-3}-2^{2}\left(-5\right)^{3}\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Divide 12 by -3 to get -4.

$$\int -4-2^{2}\left(-5\right)^{3}\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Calculate 2 to the power of 2 and get 4.

$$\int -4-4\left(-5\right)^{3}\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Calculate -5 to the power of 3 and get -125.

$$\int -4-4\left(-125\right)\left(-6+2^{3}\right)-7^{0}\mathrm{d}x$$

Multiply 4 and -125 to get -500.

$$\int -4-\left(-500\left(-6+2^{3}\right)\right)-7^{0}\mathrm{d}x$$

Calculate 2 to the power of 3 and get 8.

$$\int -4-\left(-500\left(-6+8\right)\right)-7^{0}\mathrm{d}x$$

Add -6 and 8 to get 2.

$$\int -4-\left(-500\times 2\right)-7^{0}\mathrm{d}x$$

Multiply -500 and 2 to get -1000.

$$\int -4-\left(-1000\right)-7^{0}\mathrm{d}x$$

The opposite of -1000 is 1000.

$$\int -4+1000-7^{0}\mathrm{d}x$$

Add -4 and 1000 to get 996.

$$\int 996-7^{0}\mathrm{d}x$$

Calculate 7 to the power of 0 and get 1.

$$\int 996-1\mathrm{d}x$$

Subtract 1 from 996 to get 995.

$$\int 995\mathrm{d}x$$

Find the integral of 995 using the table of common integrals rule \int a\mathrm{d}x=ax.

$$995x$$

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.

$$995x+С$$

Differentiate w.r.t. x

$$995$$