Final answer to the problem
$-\frac{3}{8}\ln\left(1+2v\right)-\frac{3}{8}\ln\left(-2v+1\right)+C_0$
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Step-by-step Solution
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1
Factor the difference of squares $1-4v^2$ as the product of two conjugated binomials
$\int\frac{3v}{\left(1+2v\right)\left(1-2v\right)}dv$
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$\int\frac{3v}{\left(1+2v\right)\left(1-2v\right)}dv$
Learn how to solve integral calculus problems step by step online. Find the integral int((3v)/(1-4v^2))dv. Factor the difference of squares 1-4v^2 as the product of two conjugated binomials. Rewrite the fraction \frac{3v}{\left(1+2v\right)\left(1-2v\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(1+2v\right)\left(1-2v\right). Multiplying polynomials.
Final answer to the problem
$-\frac{3}{8}\ln\left(1+2v\right)-\frac{3}{8}\ln\left(-2v+1\right)+C_0$