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When multiplying exponents with same base you can add the exponents: $x\left(2-x^2\right)x^4$
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$\int x^{5}\left(2-x^2\right)dx$
Learn how to solve integral calculus problems step by step online. Find the integral int(x(2-x^2)x^4)dx. When multiplying exponents with same base you can add the exponents: x\left(2-x^2\right)x^4. Rewrite the integrand x^{5}\left(2-x^2\right) in expanded form. Expand the integral \int\left(2x^{5}-x^{7}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int2x^{5}dx results in: \frac{1}{3}x^{6}.