What is the integral of 1/(v*sqrt(v^2-1)) ?

The integral of 1/(v*sqrt(v^2-1)) is arctan(sqrt(v^2-1))+C

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integral of 1/(v*sqrt(v^2-1))

\int \frac{1}{v \cdot v ^{2} - 1} d v

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

Solution steps

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

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 = v^{2} - 1

= arctan (v^{2} - 1)

Add a constant to the solution

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

f (x) = 2 x^{3}, (- 2, - 16)

\int cot (3 x) d x

ln (x x^{2} - 5)

\frac{7}{1 - x}

\frac{d}{d x} (2 e^{- x} + x e^{- x})

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