Solving: $\int\frac{6y-7}{\left(2y+1\right)\left(4y^2-1\right)}dy$
Exercise
$\int\frac{6y-7}{\left(2y+1\right)\left(4y^2-1\right)}dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int((6y-7)/((2y+1)(4y^2-1)))dy. Factor the difference of squares \left(4y^2-1\right) as the product of two conjugated binomials. When multiplying two powers that have the same base (2y+1), you can add the exponents. Rewrite the fraction \frac{6y-7}{\left(2y+1\right)^2\left(2y-1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{5}{\left(2y+1\right)^2}+\frac{-1}{2y-1}+\frac{1}{2y+1}\right)dy into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Find the integral int((6y-7)/((2y+1)(4y^2-1)))dy
Final answer to the exercise
$\frac{5}{-2\left(2y+1\right)}-\frac{1}{2}\ln\left|2y-1\right|+\frac{1}{2}\ln\left|2y+1\right|+C_0$