Solve ∫ sqrt[3]{(-2)^3-12(-2)+11}

$$\int \sqrt[ 3 ] { ( - 2 ) ^ { 3 } - 12 ( - 2 ) + 11 }$$

Evaluate

$$3x+С$$

Solution Steps

Calculate -2 to the power of 3 and get -8.

$$\int \sqrt[3]{-8-12\left(-2\right)+11}\mathrm{d}x$$

Multiply 12 and -2 to get -24.

$$\int \sqrt[3]{-8-\left(-24\right)+11}\mathrm{d}x$$

The opposite of -24 is 24.

$$\int \sqrt[3]{-8+24+11}\mathrm{d}x$$

Add -8 and 24 to get 16.

$$\int \sqrt[3]{16+11}\mathrm{d}x$$

Add 16 and 11 to get 27.

$$\int \sqrt[3]{27}\mathrm{d}x$$

Calculate \sqrt[3]{27} and get 3.

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

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

$$3x$$

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.

$$3x+С$$

Differentiate w.r.t. x

$$3$$