Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{4}}{4}+x+\frac{1}{2}\ln\left(-x+1\right)+\frac{1}{4}\ln\left(1+x^2\right)-\frac{1}{2}\arctan\left(x\right)+C_0$
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Step-by-step Solution
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1
Rewrite the expression $\frac{x^7+x^8}{x^4-1}$ inside the integral in factored form
$\int\frac{x^{7}}{-\left(1+x^2\right)\left(1-x\right)}dx$
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$\int\frac{x^{7}}{-\left(1+x^2\right)\left(1-x\right)}dx$
Learn how to solve differential calculus problems step by step online. Find the integral int((x^7+x^8)/(x^4-1))dx. Rewrite the expression \frac{x^7+x^8}{x^4-1} inside the integral in factored form. Expand. Divide x^{7} by -1-x^2+x+x^{3}. Resulting polynomial.
Final answer to the problem
$\frac{x^{5}}{5}+\frac{x^{4}}{4}+x+\frac{1}{2}\ln\left(-x+1\right)+\frac{1}{4}\ln\left(1+x^2\right)-\frac{1}{2}\arctan\left(x\right)+C_0$