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$\int\left(x^5-2x^2\right)^3\left(4x^3-5\right)^4dx$
Learn how to solve problems step by step online. Integrate the function (x^5-2x^2)^3(4x^3-5)^4. Find the integral. Rewrite the expression \left(x^5-2x^2\right)^3\left(4x^3-5\right)^4 inside the integral in factored form. The cube of a binomial (difference) is equal to the cube of the first term, minus three times the square of the first by the second, plus three times the first by the square of the second, minus the cube of the second term. In other words: (a-b)^3=a^3-3a^2b+3ab^2-b^3 = (x^{3})^3+3(x^{3})^2(-2)+3(x^{3})(-2)^2+(-2)^3 =. Multiplying polynomials x^{6} and x^{9}-6x^{6}+12x^{3}-8.