Solve ∫ left(2*xright)^22 wrt x

$$\int{ { \left(2 \times x \right) }^{ 22 } }d x$$

Evaluate

$$\frac{4194304x^{23}}{23}+С$$

Solution Steps

Factor out the constant using \int af\left(x\right)\mathrm{d}x=a\int f\left(x\right)\mathrm{d}x.

$$2^{22}\int x^{22}\mathrm{d}x$$

Since \int x^{k}\mathrm{d}x=\frac{x^{k+1}}{k+1} for k\neq -1, replace \int x^{22}\mathrm{d}x with \frac{x^{23}}{23}.

$$2^{22}\times \frac{x^{23}}{23}$$

Simplify.

$$\frac{4194304x^{23}}{23}$$

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.

$$\frac{4194304x^{23}}{23}+С$$

Differentiate w.r.t. x

$$4194304x^{22}$$