Final Answer
$\frac{x^{9}}{9}+\frac{-x^{8}}{8}+\frac{3}{7}x^{7}-\frac{5}{6}x^{6}+\frac{11}{5}x^{5}-\frac{21}{4}x^{4}+\frac{43}{3}x^{3}-\frac{85}{2}x^2+171x-\frac{1024}{3}\ln\left(x+2\right)+\frac{1}{3}\ln\left(x-1\right)+C_0$
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Step-by-step Solution
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1
Find the integral
$\int\frac{\left(x^2\right)^5}{x^2+x-2}dx$
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$\int\frac{\left(x^2\right)^5}{x^2+x-2}dx$
Learn how to solve problems step by step online. Find the integral of (x^2^5)/(x^2+x+-2). Find the integral. Simplify \left(x^2\right)^5 using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals 5. Divide x^{10} by x^2+x-2. Resulting polynomial.
Final Answer
$\frac{x^{9}}{9}+\frac{-x^{8}}{8}+\frac{3}{7}x^{7}-\frac{5}{6}x^{6}+\frac{11}{5}x^{5}-\frac{21}{4}x^{4}+\frac{43}{3}x^{3}-\frac{85}{2}x^2+171x-\frac{1024}{3}\ln\left(x+2\right)+\frac{1}{3}\ln\left(x-1\right)+C_0$