Solve ∫ sqrt{-a^3/(a-2)^2}=

$$\int \sqrt { \frac { - a ^ { 3 } } { ( a - 2 ) ^ { 2 } } } =$$

Evaluate

$$\frac{x\sqrt{-a^{3}}}{|a-2|}+С$$

Solution Steps

Find the integral of \sqrt{-\frac{a^{3}}{\left(a-2\right)^{2}}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\sqrt{-\frac{a^{3}}{\left(a-2\right)^{2}}}x$$

Simplify.

$$\frac{\sqrt{-a^{3}}x}{|a-2|}$$

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.

$$\frac{\sqrt{-a^{3}}x}{|a-2|}+С$$

Differentiate w.r.t. x

$$\frac{\sqrt{-a^{3}}}{|a-2|}$$