Solve ∫ 4az/sqrt{z^4-25z^2}=

$$\int \frac { 4 a z } { \sqrt { z ^ { 4 } - 25 z ^ { 2 } } } =$$

Evaluate

$$\frac{4axz}{|z|\sqrt{z^{2}-25}}+С$$

$$|z|>5$$

Solution Steps

Find the integral of \frac{4az}{\sqrt{z^{4}-25z^{2}}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{4az}{\sqrt{z^{4}-25z^{2}}}x$$

Simplify.

$$\frac{4azx}{\sqrt{z^{4}-25z^{2}}}$$

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.

$$\frac{4azx}{\sqrt{z^{4}-25z^{2}}}+С$$

Differentiate w.r.t. x

$$\frac{4az}{|z|\sqrt{z^{2}-25}}$$

$$|z|>5$$