Final answer to the problem
Step-by-step Solution
Specify the solving method
Divide $y^5$ by $1-y^4$
Learn how to solve integrals of rational functions problems step by step online.
$\begin{array}{l}\phantom{-y^{4}+1;}{-y\phantom{;}\phantom{-;x^n}}\\-y^{4}+1\overline{\smash{)}\phantom{;}y^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-y^{4}+1;}\underline{-y^{5}\phantom{-;x^n}\phantom{-;x^n}\phantom{-;x^n}+y\phantom{;}\phantom{-;x^n}}\\\phantom{-y^{5}+y\phantom{;};}\phantom{;}y\phantom{;}\phantom{-;x^n}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((y^5)/(1-y^4))dy. Divide y^5 by 1-y^4. Resulting polynomial. Expand the integral \int\left(-y+\frac{y}{1-y^4}\right)dy into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-ydy results in: -\frac{1}{2}y^2.