Final Answer
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Expand the integral $\int\left(2x^5-10x^3-2x^2+\frac{10}{x^2-5}\right)dx$ into $4$ integrals using the sum rule for integrals, to then solve each integral separately
Learn how to solve integrals of polynomial functions problems step by step online.
$\int2x^5dx+\int-10x^3dx+\int-2x^2dx+\int\frac{10}{x^2-5}dx$
Learn how to solve integrals of polynomial functions problems step by step online. Integrate int(2x^5-10x^3-2x^210/(x^2-5))dx. Expand the integral \int\left(2x^5-10x^3-2x^2+\frac{10}{x^2-5}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. Factor the difference of squares x^2-5 as the product of two conjugated binomials. Rewrite the fraction \frac{10}{\left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right)} in 2 simpler fractions using partial fraction decomposition. Find the values for the unknown coefficients: A, B. The first step is to multiply both sides of the equation from the previous step by \left(x+\sqrt{5}\right)\left(x-\sqrt{5}\right).