Solve ∫ 1/(x^2+1)(x^2-1)dt

$$\int \frac { 1 } { ( x ^ { 2 } + 1 ) ( x ^ { 2 } - 1 ) } d t$$

Evaluate

$$\frac{t}{x^{4}-1}+С$$

Solution Steps

Find the integral of \frac{1}{\left(x^{2}+1\right)\left(x^{2}-1\right)} using the table of common integrals rule \int a\mathrm{d}t=at.

$$\frac{t}{\left(x^{2}+1\right)\left(x^{2}-1\right)}$$

If F\left(t\right) is an antiderivative of f\left(t\right), then the set of all antiderivatives of f\left(t\right) is given by F\left(t\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\frac{t}{\left(x^{2}+1\right)\left(x^{2}-1\right)}+С$$

Differentiate w.r.t. x

$$-\frac{4tx^{3}}{\left(x^{4}-1\right)^{2}}$$