integral of (t^2-1)/(t^4-1) — step-by-step solution

Before performing the integration, let's calculate:

\frac{t^{2} - 1}{t^{4} - 1}

Using the formula:

a^{2} - b^{2} = (a - b) \cdot (a + b)

, we simplify the fraction:

\frac{t^{2} - 1}{t^{4} - 1}

by the common factor:

t^{2} - 1

to get the new quotient:

\frac{1}{t^{2} + 1}

Let's integrate:

\int \frac{1}{t^{2} + 1} d t

ⓘ The derivative of

\arctan (t)

\frac{1}{t^{2} + 1}

, so

\arctan (t)

is an antiderivative of

\frac{1}{t^{2} + 1}

\int \frac{1}{t^{2} + 1} d t

\arctan (t)

\arctan (t)

▶Indefinite integrals are defined up to an additive constant C, so this yields:

\arctan (t) + C