Solving: $\int\frac{2}{4-y^2}dy$
Exercise
$\int\left(\frac{2}{4-y^2}\right)dx$
Step-by-step Solution
Learn how to solve problems step by step online. Find the integral int(2/(4-y^2))dy. Rewrite the expression \frac{2}{4-y^2} inside the integral in factored form. Rewrite the fraction \frac{2}{\left(2+y\right)\left(2-y\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2\left(2+y\right)}+\frac{1}{2\left(2-y\right)}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{2\left(2+y\right)}dy results in: \frac{1}{2}\ln\left(y+2\right).
Find the integral int(2/(4-y^2))dy
Final answer to the exercise
$\frac{1}{2}\ln\left|y+2\right|-\frac{1}{2}\ln\left|-y+2\right|+C_0$