First, we can recognize that the integrand is a standard form of the arctangent function, namely:
$$\frac{1}{x^2+c^2}=\frac{1}{c^2}\cdot\frac{1}{1+(x/c)^2}$$
Using the substitution $u=x/c$, we get:
$$\int_{0}^{c} \frac{d x}{x^{2}+c^{2}}=\int_{0}^{1}
Show more…