Solve ∫ tan^-1sqrt{1-n/1+n}

$$\int \tan ^ { - 1 } \sqrt { \frac { 1 - n } { 1 + n } }$$

Evaluate

$$\arctan(\sqrt{\frac{1-n}{n+1}})x+С$$

Solution Steps

Find the integral of \arctan(\sqrt{\frac{1-n}{1+n}}) using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\arctan(\sqrt{\frac{1-n}{1+n}})x$$

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.

$$\arctan(\sqrt{\frac{1-n}{1+n}})x+С$$

Differentiate w.r.t. x

$$\arctan(\sqrt{\frac{1-n}{n+1}})$$