Solve ∫ left(x^2right)^2^2 wrt x

$$\int{ { \left( { x }^{ 2 } \right) }^{ { 2 }^{ 2 } } }d x$$

Evaluate

$$\frac{x^{9}}{9}+С$$

Solution Steps

Calculate 2 to the power of 2 and get 4.

$$\int \left(x^{2}\right)^{4}\mathrm{d}x$$

To raise a power to another power, multiply the exponents. Multiply 2 and 4 to get 8.

$$\int x^{8}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{8}\mathrm{d}x with \frac{x^{9}}{9}.

$$\frac{x^{9}}{9}$$

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.

$$\frac{x^{9}}{9}+С$$

Differentiate w.r.t. x

$$x^{8}$$