Resolved: "Evaluate the following integral: ∫vdv6v2−1"

Tobias Ali

Answered question

2021-05-30

Evaluate the following integral:

\int \frac{v d v}{6 v^{2} - 1}

Leonard Stokes

Skilled2021-05-31Added 98 answers

Evaluate as follows:
Substitute

6 v^{2} - 1 = t

Differentiate with respect to v,

12 v = \frac{d t}{d v}

v d v = \frac{d t}{12}

Thus, the integral is calculated as:

I = \int \frac{v d v}{6 v^{2} - 1}

= \int \frac{d t}{12 t}

= \frac{1}{12} \log | t | + c

= \frac{1}{12} \log | 6 v^{2} - 1 | + c

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