What is the integral of 1/((tsqrt(t^2-1))) ?

The integral of 1/((tsqrt(t^2-1))) is arctan(sqrt(t^2-1))+C

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integral of 1/((tsqrt(t^2-1)))

integral

\frac{1}{( t t ^{2} - 1 )}

arctan (t^{2} - 1) + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u ^{2} + 1} d u

= \int \frac{1}{u ^{2} + 1} d u

Use the common integral:

\int \frac{1}{u ^{2} + 1} d u = arctan (u)

= arctan (u)

Substitute back

u = t^{2} - 1

= arctan (t^{2} - 1)

Add a constant to the solution

= arctan (t^{2} - 1) + C

(x + 1)^{- 3}

\frac{1}{a + x ^{2}}

((e)^{x})^{2}

cos^{2} (t) sin (t)

((sin (x))^{2}) ((cos^{2} (x))^{2})

What is the integral of 1/((tsqrt(t^2-1))) ?
The integral of 1/((tsqrt(t^2-1))) is arctan(sqrt(t^2-1))+C